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1.1 Introduction to obvious area1.2 Apparent areas of aqueduct cross-sections and farms1.3 Introduction to volume1.4 Introduction to flow-rate1.5 Introduction to allotment and per mil1.6 Introduction to graphs1.7 Test your data

1.1.1 Triangles1.1.2 Squares and Rectangles1.1.3 Rhombuses and Parallelograms1.1.4 Trapeziums1.1.5 Circles1.1.6 Metric Conversions

It is vital to have the ability to admeasurement and account obvious areas. It potential be all-important to calculate, for instance, the obvious breadth of the array of a aqueduct or the obvious breadth of a farm.

This Section will altercate the including of a number of the greatest accepted obvious areas: the triangle, the sq., the rectangle, the rhombus, the parallelogram, the trapezium and the amphitheater (see Fig. 1a).

Fig. 1a. The greatest accepted obvious areas

The acme (h) of a triangle, a rhombus, a parallelogram or a trapezium, is the ambit from a prime bend to the opposed ancillary alleged abject (b). The acme is persistently erect to the bottom; in added phrases, the acme makes a “proper angle” with the bottom. An archetype of a acceptable bend is the bend of this web page.

In the case of a aboveboard or a rectangle, the announcement breadth (1) is regularly acclimated as a substitute of abject and amplitude (w) as a substitute of top. In the case of a amphitheater the announcement diametre (d) is acclimated (see Fig. 1b).

Fig. 1b. The acme (h), abject (b), amplitude (w), breadth (1) and diametre (d) of the very best accepted obvious areas

The obvious breadth or obvious (A) of a triangle is affected by the components:

A (triangle) = 0.5 x abject x acme = 0.5 x b x h ….. (1)

Triangles can purchase abounding shapes (see Fig. 2) however the aforementioned blueprint is acclimated for all of them.

Fig. 2. Some examples of triangles

EXAMPLE

Calculate the obvious breadth of the triangles no. 1, no. 1a and no. 2

Given

Triangles no. 1 and no. 1a:

base = 3 cmheight = 2 cm

Formula:

A = 0.5 x abject x top= 0.5 x 3 cm x 2 cm = 3 cm2

Triangle no. 2:

base = 3 cmheight = 2 cm

A = 0.5 x 3 cm x 2 cm = 3 cm2

It might be obvious that triangles no. 1, no. 1a and no. 2 purchase the aforementioned floor; the shapes of the triangles are totally different, however the abject and the acme are in all three circumstances the identical, so the obvious is similar.

The obvious of those triangles is bidding in aboveboard centimetres (written as cm2). Apparent areas can moreover be bidding in aboveboard decimetres (dm2), aboveboard metres (m2), and so forth…

QUESTION

Calculate the obvious areas of the triangles nos. 3, 4, 5 and 6.

Given

Triangle no. 3:

base = 3 cmheight = 2 cm

Formula:

A = 0.5 x abject x top= 0.5 x 3 cm x 2 cm = 3 cm2

Triangle no. 4:

base = 4 cmheight = 1 cm

A = 0.5 x 4 cm x 1 cm = 2 cm2

Triangle no. 5:

base = 2 cmheight = 3 cm

A = 0.5 x 2 cm x 3 cm = 3 cm2

Triangle no. 6:

base = 4 cmheight = 3 cm

A = 0.5 x 4 cm x 3 cm = 6 cm2

The obvious breadth or obvious (A) of a aboveboard or a rectangle is affected by the components:

A (sq. or rectangle) = breadth x amplitude = l x w ….. (2)

In a aboveboard the lengths of all 4 abandon are in accordance and all 4 angles are acceptable angles.

In a rectangle, the lengths of the opposed abandon are in accordance and all 4 angles are acceptable angles.

Fig. 3. A aboveboard and a rectangle

Note that in a aboveboard the breadth and amplitude are in accordance and that in a rectangle the breadth and amplitude usually are not in accordance (see Fig. 3).

QUESTION

Calculate the obvious areas of the rectangle and of the aboveboard (see Fig. 3).

Given

Square:

size = 2 cmwidth = 2 cm

Formula:

A = breadth x width= 2 cm x 2 cm = 4 cm2

Rectangle:

size = 5 cmwidth = 3 cm

Formula:

A = breadth x width= 5 cm x 3 cm = 15 cm2

Related to irrigation, you’ll typically seem past the announcement hectare (ha), which is a obvious breadth unit. By definition, 1 hectare equals 10 000 m2. For instance, a acreage with a breadth of 100 m and a amplitude of 100 m2 (see Fig. 4) has a obvious breadth of 100 m x 100 m = 10 000 m2 = 1 ha.

Fig. 4. One hectare equals 10 000 m2

The obvious breadth or obvious (A) of a rhombus or a parallelogram is affected by the components:

A (rhombus or parallelogram) = abject x acme = b x h ….. (3)

In a rhombus the lengths of all 4 abandon are equal; not one of the angles are acceptable angles; opposed abandon run parallel.

In a parallelogram the lengths of the opposed abandon are equal; not one of the angles are acceptable angles; opposed abandon run alongside (see Fig. 5).

Fig. 5. A rhombus and a parallelogram

QUESTION

Calculate the obvious areas of the rhombus and the parallelogram (see Fig. 5).

Given

Rhombus:

base = 3 cmheight = 2 cm

Formula:

A = abject x top= 3 cm x 2 cm = 6 cm2

Parallelogram:

base = 3.5 cmheight = 3 cm

Formula:

A = abject x top= 3.5 cm x 3 cm = 10.5 cm2

The obvious breadth or obvious (A) of a trapezium is affected by the components:

A (trapezium) = 0.5 (base prime) x acme = 0.5 (b a) x h ….. (4)

The prime (a) is the ancillary opposed and alongside to the abject (b). In a trapezium alone the abject and the highest run parallel.

Some examples are obvious in Fig. 6:

Fig. 6. Some examples of trapeziums

EXAMPLE

Calculate the obvious breadth of trapezium no. 1.

Given

Trapezium no. 1:

base = 4 cmtop = 2 cmheight = 2 cm

Formula:

A = 0.5 x (base x prime) x top= 0.5 x (4 cm 2 cm) x 2 cm= 0.5 x 6 cm x 2 cm = 6 cm2

QUESTION

Calculate the obvious areas trapeziums nos. 2, 3 and 4.

Given

Trapezium no. 2:

base = 5 cmtop = 1 cmheight = 2 cm

Formula:

A = 0.5 x (base prime) x top= 0.5 x (5 cm 1 cm) x 2 cm= 0.5 x 6 cm x 2 cm = 6 cm2

Trapezium no. 3:

base = 3 cmtop = 1 cmheight = 1 cm

A = 0.5 x (3 cm 1 cm) x 2 cm= 0.5 x 4 cm x 2 cm = 4 cm2

Trapezium no. 4:

base = 2 cmtop = 4 cmheight = 2 cm

A = 0.5 x (2 cm 4 cm) x 2 cm= 0.5 x 6 cm x 2 cm = 6 cm2

Note that the obvious areas of the trapeziums 1 and 4 are equal. Cardinal 4 is the aforementioned as cardinal 1 however the other way up.

Another adjustment to account the obvious breadth of a trapezium is to bisect the trapezium right into a rectangle and two triangles, to admeasurement their abandon and to actuate alone the obvious areas of the rectangle and the 2 triangles (see Fig. 7).

Fig. 7. Splitting a trapezium into one rectangle and two triangles. Agenda that A = A1 A2 A3 = 1 6 2 = 9 cm2

The obvious breadth or obvious (A) of a amphitheater is affected by the components:

A (circle) = 1/4 (p x d x d) = 1/4 (p x d2) = 1/4 (3.14 x d2) ….. (5)

whereby d is the bore of the amphitheater and p (a Greek letter, arresting Pi) a related (p = 3.14). A bore (d) is a beeline band which divides the amphitheater in two in accordance elements.

Fig. 8. A circle

EXAMPLE

Given

Circle: d = 4.5 cm

Formula:

A = 1/4 (p x d²) = 1/4 (3.14 x d x d)= 1/4 (3.14 x 4.5 cm x 4.5 cm)= 15.9 cm2

QUESTION

Calculate the obvious breadth of a amphitheater with a bore of three m.

Given

Circle: d = 3 m

Formula:

A = 1/4 (p x d²) = 1/4 (3.14 x d x d) = 1/4 (3.14 x 3 m x 3 m) = 7.07 m2

i. Units of size

The basal assemblage of breadth within the metric association is the accent (m). One accent might be disconnected into 10 decimetres (dm), 100 centimetres (cm) or 1000 millimetres (mm); 100 m equals to 1 hectometre (hm); whereas 1000 m is 1 kilometre (km).

1 km = 10 hm = 1000 m0.1 km = 1 hm = 100 m0.01 km = 0.1 hm = 10 m0.001 km = 0.01 hm = 1 m

ii. Units of floor

The basal assemblage of breadth within the metric association is the aboveboard accent (m), which is acquired by including a breadth of 1 accent by a amplitude of 1 accent (see Fig. 9).

Fig. 9. A aboveboard metre

1 km2 = 100 ha2 = 1 000 000 m20.01 km2 = 1 ha2 = 10 000 m20.000001 km2 = 0.0001 ha2 = 1 m2

NOTE:

1 ha = 100 m x 100 m = 10 000 m2

1.2.1 Determination of the obvious areas of aqueduct cross-sections1.2.2 Determination of the obvious breadth of a farm

This Section explains easy methods to administer the obvious breadth formulation to 2 accepted utilized issues that may typically be met within the area.

The greatest accepted look of a aqueduct array is a trapezium or, added actually, an “up-side-down” trapezium (see Fig. 10).

Fig. 10. Aqueduct cross-section

The breadth (A B C D), hatched on the aloft drawing, is alleged the aqueduct array and has a trapezium look (evaluate with trapezium no. 4). Thus, the blueprint to account its obvious is agnate to the blueprint acclimated to account the obvious breadth of a trapezium (components 4):

Surface breadth of the aqueduct array = 0.5 (base prime line) x aqueduct abyss = 0.5 (b a) x h ….. (6)

whereby:

prime band (a) = prime amplitude of the canal

canal abyss (h) = acme of the aqueduct (from the basal of the aqueduct to the highest of the embankment)

Suppose that the aqueduct comprises water, as obvious in Fig. 11.

Fig. 11. Wetted array of a canal

The breadth (A B C D), hatched on the aloft drawing, is alleged the wetted aqueduct array or wetted cross-section. It moreover has a trapezium look and the blueprint to account its obvious breadth is:

Surface breadth of the wetted aqueduct array = 0.5 (base prime line) x baptize abyss = 0.5 (b a1) x h1 ….. (7)

whereby:

prime band (a1) = prime amplitude of the baptize degree

water abyss (h1) = the acme or abyss of the baptize within the aqueduct (from the basal of the aqueduct to the baptize degree).

EXAMPLE

Calculate the obvious breadth of the array and the wetted cross-section, of the aqueduct obvious in Fig. 12 under.

Fig. 12. Dimensions of the cross-section

Given

Canal cross-section:

base (b) = 1.25 mtop band (a) = 3.75 mcanal abyss (h) = 1.25 m

Formula:

A = 0.5 x (b a) x h= 0.5 x (1.25 m 3.75 m) x 1.25 m= 3.125 m2

Canal wetted cross-section:

base (b) = 1.25 mtop band (a1) = 3.25 mwater abyss (h1) = 1.00 m

Formula:

A = 0.5 x (b a1) x h= 0.5 x (1.25 m 3.25 m) x 1.00 m= 2.25 m2

It could also be all-important to actuate the obvious breadth of a farmer’s area. For instance, again clever how ample irrigation baptize ought to be accustomed to a assertive area, the admeasurement of the acreage cost be identified.

When the looks of the acreage is accredited and has, for instance, a ellipsoidal form, it shouldn’t be too troublesome to account the obvious breadth already the breadth of the acreage (that’s the abject of its accredited form) and the amplitude of the acreage purchase been abstinent (see Fig. 13).

Fig. 13. Acreage of accredited form

EXAMPLE

Given

Length of the acreage = 50 mWidth of the acreage = 30 m

Formula:

A = breadth x amplitude (components 2)= 50 m x 30 m = 1500 m2

QUESTION

What is the breadth of the aforementioned area, bidding in hectares?

Section 1.1.2 defined {that a} hectare is in line with 10 000 m. Thus, the blueprint to account a obvious breadth in hectares is:

….. (8)

In this case: breadth of the acreage in

More usually, nevertheless, the acreage look is just not common, as obvious in Fig. 14a.

Fig. 14a. Acreage of aberrant form

In this case, the acreage ought to be disconnected in a number of accredited areas (sq., rectangle, triangle, and so forth.), as has been performed in Fig. 14b.

Fig. 14b. Division of aberrant acreage into accredited areas

Surface breadth of the sq.: As = breadth x amplitude = 30 m x 30 m = 900 m2Surface breadth of the rectangle: Ar = breadth x amplitude = 50 m x 15 m = 750 m2Surface breadth of the triangle: At = 0.5 x abject x acme = 0.5 x 20 m x 30 m = 300 m2Total obvious breadth of the sector: A = As Ar At = 900 m2 750 m2 300 m2 = 1950 m2

1.3.1 Units of volume1.3.2 Aggregate of baptize on a area

A mixture (V) is the agreeable of a anatomy or object. Booty for archetype a block (Fig 15). A block has a assertive breadth (l), amplitude (w) and acme (h). With these three information, the combination of the block might be affected utility the components:

V (block) = breadth x amplitude x acme = l x w x h ….. (9)

Fig. 15. A block

EXAMPLE

Calculate the combination of the aloft block.

Given

size = 4 cmwidth = 3 cmheight = 2 cm

Formula:

V = breadth x amplitude x top= 4 cm x 3 cm x 2 cm= 24 cm3

The mixture of this block is bidding in cubic centimetres (written as cm). Volumes can moreover be bidding in cubic decimetres (dm3), cubic metres (m3), and so forth.

QUESTION

Calculate the combination in m3 of a block with a breadth of 4 m, a amplitude of fifty cm and a acme of 200 mm.

Given

All abstracts cost be tailored in metres (m)

size = 4 mwidth = 50 cm = 0.50 mheight = 200 mm = 0.20 m

Formula:

V = breadth x amplitude x top= 4 m x 0.50 m x 0.20 m= 0.40 m3

QUESTION

Calculate the combination of the aforementioned block, this time in cubic centimetres (cm3)

Given

All abstracts cost be tailored in centimetres (cm)

size = 4 m = 400 cmwidth = 50 cmheight = 200 mm = 20 cm

Formula:

V = breadth x amplitude x top= 400 cm x 50 cm x 20 cm= 400 000 cm3

Of course, the aftereffect is similar: 0.4 m3 = 400 000 cm3

The basal assemblage of mixture within the metric association is the cubic accent (m3) which is acquired by including a breadth of 1 metre, by a amplitude of 1 accent and a acme of 1 accent (see Fig. 16).

Fig. 16. One cubic metre

NOTE

and

Suppose a one-litre canteen is abounding with water. The mixture of the baptize is appropriately 1 litre or 1 dm3. Back the canteen of baptize is emptied on a desk, the baptize will advance out over the desk and anatomy a attenuate baptize layer. The bulk of baptize on the desk is the aforementioned as the majority of baptize that was within the bottle; actuality 1 litre.

The mixture of baptize charcoal the identical; alone the looks of the “water physique” adjustments (see Fig. 17).

Fig. 17. One litre of baptize advance over a desk

A agnate motion occurs for those who advance irrigation baptize from a accumulator backlog over a farmer’s area.

QUESTION

Suppose there’s a reservoir, abounding with water, with a breadth of 5 m, a amplitude of 10 m and a abyss of two m. All the baptize from the backlog is advance over a acreage of 1 hectare. Account the baptize abyss (which is the array of the baptize layer) on the sector, see Fig. 18.

Fig. 18. A mixture of 100 m3 of baptize advance over an breadth of 1 hectare

The blueprint to make use of is:

….. (10)

As the aboriginal step, the combination of baptize cost be calculated. It is the combination of the abounding reservoir, affected with blueprint (9):

As the extra step, the array of the baptize band is affected utility blueprint (10):

Given

Surface of the acreage = 10 000 m2 Aggregate of baptize = 100 m3

Formula:

QUESTION

A baptize band 1 mm blubbery is advance over a acreage of 1 ha. Account the combination of the baptize (in m3), with the recommendation of Fig. 19.

Fig. 19. One millimetre baptize abyss on a acreage of 1 hectare

The blueprint to make use of is:

Volume of baptize (V) = Apparent of the acreage (A) x Baptize abyss (d) ….. (11)

Given

Surface of the acreage = 10 000 m2Water abyss = 1 mm =1/1 000 = 0.001 m

Formula: Aggregate (m³)

= obvious of the acreage (m²) x baptize abyss (m) V = 10 000 m2 x 0.001 mV = 10 m3 or 10 000 litres

The flow-rate of a river, or of a canal, is the combination of baptize absolved by means of this river, or this canal, throughout a accustomed aeon of time. Related to irrigation, the combination of baptize is often bidding in litres (l) or cubic metres (m3) and the time in irregular (s) or hours (h). The flow-rate is moreover alleged discharge-rate.

The baptize lively out of a faucet fills a one litre canteen in a single second. Appropriately the breeze quantity (Q) is one litre per further (1 l/s) (see Fig. 20).

Fig. 20. A flow-rate of 1 litre per second

QUESTION

The baptize provided by a pump fills a growth of 200 litres in 20 seconds. What is the breeze quantity of this pump?

The blueprint acclimated is:

….. (12a)

Given

Volume of water: 200 lTime: 20 s

Formula:

The assemblage “litre per second” is regularly acclimated for child flows, e.g. a faucet or a child ditch. For past flows, e.g. a river or a capital canal, the assemblage “cubic accent per second” (m3/s) is added calmly used.

QUESTION

A river discharges 100 m3 of baptize to the ocean each 2 seconds. What is the flow-rate of this river bidding in m3/s?

The blueprint acclimated is:

….. (12b)

Given

Volume of water: 100 m3Time: 2 s

Formula:

The acquittal quantity of a pump is usually bidding in m3 per hour (m3/h) or in litres per minute (l/min).

….. (12c)

….. (12d)

NOTE: Blueprint 12a, 12b, 12c and 12d are the identical; alone the items change

1.5.1 Percentage1.5.2 Per mil

In affiliation to agriculture, the phrases allotment and per mil will likely be met usually. For occasion “60 % of absolutely the breadth is anhydrous in the course of the dry season”. In this Section the acceptation of the phrases “share” and “per mil” will likely be mentioned.

The chat “share” company really “per hundred”; in added phrases one % is the one hundredth allotment of the whole. You can both deal with %, or %, or 1/100, or 0.01.

Some examples are:

QUESTION

How abounding oranges are 1% of a absolute of 300 oranges? (see Fig. 21)

Fig. 21. Three oranges are 1% of 300 oranges

1% of 300 oranges = 1/100 x 300 = 3 oranges

QUESTIONS

6% of 100 cows

6/100 x 100 = 6 cows

15% of 28 hectares

15/100 x 28 = 4.2 ha

80/100 x 90 = 72 tasks

150% of a account bacon of \$100

150/100 x 100 = 1.5 x 100 = \$150

0.5% of 194.5 litres

0.5/100 x 194.5 = 0.005 x 194.5 = 0.9725 litres

The chat “per mil” company really “per thousand”; in added phrases one per mil is one thousandth allotment of the whole.

You can both write: per mil, or , or 1/1000, or 0.001.

Some examples are:

QUESTION

How abounding oranges are 4 of 1000 oranges? (see Fig. 22)

Fig. 22. Four oranges are 4 of 1000 oranges

4 of 1000 oranges = 4/1000 x 1000 = 4 oranges

NOTE

as a result of 10 = 10/1000 = 1/10 = 1%

QUESTIONS

3 of three 000 oranges

3/1000 x 3 000 = 9 oranges

35 of 10 000 ha

35/1000 x 10 000 = 350 ha

0.5 of 750 km2

0.5/1000 x 750 =0.375 km2

1.6.1 Archetype 11.6.2 Archetype 2

A blueprint is a cartoon through which the accord amid two (or extra) objects of recommendation (e.g. time and bulb progress) is obvious in a allegorical method.

To this finish, two ambit are fatigued at a acceptable angle. The accumbent one is alleged the x arbor and the vertical one is alleged the y axis.

Where the x arbor and the y arbor bisect is the “0” (zero) level (see Fig. 23).

The acute of the recommendation on the blueprint is mentioned within the afterward examples.

Fig. 23. A graph

Suppose it’s all-important to perform a blueprint of the advance quantity of a maize plant. Each anniversary the acme of the bulb is measured. One anniversary afterwards burying the seed, the bulb measures 2 cm in top, two weeks afterwards burying it measures 5 cm and three weeks afterwards burying the acme is 10 cm, as illustrated in Fig. 24a.

Fig. 24a. Measuring the advance quantity of a maize plant

These after-effects might be suggested on a graph. The time (in weeks) will likely be adumbrated on the x axis; 2 cm on the arbor represents 1 week. The bulb acme (in centimetres) will likely be adumbrated on the y axis; 1 cm on the arbor represents 1 cm of bulb top.

After 1 anniversary the acme is 2 cm; that is adumbrated on the blueprint with A; afterwards 2 weeks the acme is 5 cm, see B, and afterwards 3 weeks the acme is 10 cm, see C, as obvious in Fig. 24b.

At burying (Time = 0) the acme was zero, see D.

Now affix the crosses (see Fig. 24c) with a beeline line. The band signifies the advance quantity of the plant; that is the acme entry over time.

Fig. 24b. Advance quantity of a maize plant

It might be obvious from the blueprint that the bulb is rising sooner and sooner (in the course of the aboriginal anniversary 2 cm and in the course of the third anniversary 5 cm); the band from B to C is steeper than the band from D to A.

From the blueprint might be apprehend what the acme of the bulb was after, say 2 1/2 weeks; see the dotted band (Fig. 24c). Locate on the accumbent arbor 2 1/2 weeks and chase the dotted band upwards till the dotted band crosses the graph. From this bridge chase the dotted band to the larboard till the vertical arbor is reached. Now booty the studying: 7.5 cm, which company that the bulb had a acme of seven.5 cm afterwards 2 1/2 weeks. This acme has not been abstinent in actuality, however with the blueprint the acme might be bent anyway.

QUESTION

What was the acme of the bulb afterwards 1 1/2 weeks?

The acme of the bulb afterwards 1 1/2 weeks was 3.5 cm (see Fig. 24c).

Fig. 24c. Blueprint of the advance quantity of a maize plant

Another archetype to allegorize how a blueprint ought to be fabricated is the aberration of the temperature over one abounding day (24 hours). Suppose the alfresco temperature (at all times within the shade) is measured, with a thermometer, each two hours, beginning at midnight and disaster the afterward midnight.

Suppose the afterward after-effects are discovered:

Time (hr)

Temperature (°C)

0

16

2

13

4

6

6

8

8

13

10

19

12

24

14

28

16

2

18

27

20

22

22

19

24

16

On the x arbor announce the time in hours, whereby 1 cm on the blueprint is 2 hours. On the y arbor announce the temperature in levels Celsius (°C), whereby 1 cm on the blueprint is 5°C.

Now announce (with crosses) the ethics from the desk (above) on the blueprint cardboard and affix the crosses with beeline dotted ambit (see Fig. 25a).

Fig. 25a. Blueprint assuming temperature over 24 hours; aberration 16 hour studying

At this stage, for those who attending anxiously on the graph, you’ll agenda that there’s a precise brusque change in its look concerning the sixteenth hour. The alfresco temperature appears to amass collapsed from 28°C to 2°C in two hours time! That doesn’t accomplish sense, and the account of the thermometer on the sixteenth hour cost purchase been unsuitable. This cantankerous can’t be taken in utility for the blueprint and ought to be rejected. The alone dotted band we are able to purchase is the beeline one in amid the account on the fourteenth hour and the account on the eighteenth hour (see Fig. 25b).

Fig. 25b. Blueprint assuming temperature over 24 hours; estimated alteration of mistake

In absoluteness the temperature will change added step by step than adumbrated by the dotted line; that’s the reason a bland ambit is fabricated (steady line). The bland ambit represents the very best astute approximation of the temperature over 24 hours (see Fig. 25c).

Fig. 25c. Blueprint assuming temperature over 24 hours; bland curve

From the blueprint it may be obvious that the minimal or everyman temperature was completed about 4 o’clock within the morning and was about 6°C. The completed temperature was completed at 4 o’clock within the afternoon and was about 29°C.

QUESTION

What was the temperature at 7, 15 and 23 hours? (Always use the tasteless ambit to booty the readings).

Temperature at 7 hours: 10°CTemperature at 15 hours: 29°CTemperature at 23 hours: 17°C

1) Account the obvious areas of the afterward triangles:

2) Account the obvious areas of the afterward trapeziums:

3) Account the array of the aqueduct again given:

4) Account the wetted array again in accession to three) is accustomed that the baptize acme is 0.8 m and the highest amplitude of the baptize obvious is 2.32 m.

5) A ellipsoidal acreage has a breadth of 120 m and a amplitude of 85 m. What is the breadth of the acreage in hectares?

6)

7) Account the combination of the afterward blocks, again given:

8) Account the combination of baptize (in m3) on a area, again given: the breadth = 150 m, the amplitude = 56 m and the baptize band = 70 mm.

9) Account the minimal abyss of a reservoir, which has: a breadth of 15 m and a amplitude of 10 m and which has to accommodate 50 mm baptize for a acreage of 175 m continued and 95 m large.

10) Accomplish a blueprint of the account condensate over a aeon of 1 12 months, again given:

Month

Rain (mm/month)

Jan.

42

Feb.

65

Mar.

140

Apr.

120

May

76

June

24

July

6

Aug.

0

Sept.

0

Oct.

10

Nov.

17

Dec.

27

1)

2)

3) A = 0.5 x (b a) x h = 0.5 x (1.2 m 2.6 m) x 1 m = 1.9 m2

4) A = 0.5 x (b a1) x h1 – 0.5 x (1.2 m 2.32 m) x 0.8 m = 1.408 m2

5) Breadth of the acreage in aboveboard metres = l (m) x w (m) = 120 m x 85 m = 10 200 m2

6)

7)

8) V = l x w x h = 150 m x 56 m x 0.070 m = 588 m3

9)

Volume of the reservoir: V = 831.25 m3 = breadth of backlog (m) x amplitude of backlog (m) x abyss of backlog (m)

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