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A heap of wheat is in the form of a cone of diameter $9 m$ and height $3.5 m .$ Find its volume. How much canvas cloth is required to just cover the heap?

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47.74 c m 3

and

80.54 c m 2

74.18 c m 3

and

64.57 c m 2

94.48 c m 3

and

80.54 c m 2

74.18 c m 3

and

80.54 c m 2

answer is D.

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Detailed Solution

Given that the diameter of the cone is 9 m and its height is 3.5 m.
We have to find the volume of the cone and the amount of canvas required to cover the heap, i.e., the curved surface area of the cone.
The volume of a circular cone is expressed as,

V = 13 π r 2 h

, where

r

be the radius of a circular cone.
The radius, r will be,
Question Image

The slant height, l of the cone is,
Question Image

So, the volume of the cone, V is,
Question Image

Thus, the curved surface area, A of the cone is,
Question Image

The volume of the cone and the canvas required to cover the heap of wheat is

74.18 c m 3

and

80.54 c m 2

.
Therefore, the correct option is 4.

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