Question

In a field, dry fodder for the cattle is heaped in a conical shape. The height of the cone is
2.1m. and diameter of base is 7.2 m. Find the volume of the fodder. if it is to be covered
by polythin in rainy season then how much minimum polythin sheet is needed ?
$\pi$
=(22/7 and 17.37=4.17
​

Answer 1

Answer:

Given: Height of the heap (h) = 2.1 m, diameter of the base (d) = 7.2 m

∴ Radius of the base (r) = d/2 = 7.2/2 = 3.6 m To find: Volume of the heap of the fodder and polythene sheet required

i. Volume of the heap of fodder = (1/3) πr2h

= (1/3) x (22/7) x (3.6)2 x 2.1

= (1/3) x (22/7) x 3.6 x 3.6 x 2.1

= 1 x 22 x 1.2 x 3.6 x 0.3

= 28.51 cubic metre

ii. Now, l2 = r2 + h2

= (3.6)2 + (2.1)2

= 12.96 + 4.41

∴ l2 =17.37

∴ l2 = √17.37 ... [Taking square root on both sides] = 4.17 m

iii. Area of the polythene sheet needed to cover the heap of the fodder = Curved surface area of the conical heap

= πrl

= (22/7) x 3.6 x 4.17

= 47.18 sq.m

∴ The volume of the heap of the fodder is 28.51 cubic metre and a polythene sheet of 47.18 sq.m will be required to cover it.

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