Question

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? (Use $\mathrm{\pi }=3.14$).

Answer 1

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cone =

Here, the diameter is given as 9 m. From this we get the base radius as r = 4.5 m.

Substituting the values of r = 4.5 m and h = 3.5 m in the above equation and using π = 3.14

Volume =

=

= 74.1825

Hence the volume of the given cone with the specified dimensions is

The amount of canvas required to cover the conical heap would be equal to the curved surface area of the conical heap.

The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as

Curved Surface Area = πrl

To find the slant height ‘l’ to be used in the formula for Curved Surface Area we use the following relation

Slant height, l =

=

=

=

Hence the slant height l of the conical heap is m.

Now, substituting the values of r = 4.5 m and slant height l = m and using in the formula of C.S.A,

We get Curved Surface Area =

= 80.55

Hence the amount of canvas required to just cover the heap would be