Question

Find the length of cloth used in making a conical pandal of height 100 m and base radius 240 m, if the cloth is 100$\mathrm{\pi }$ m wide.

Answer 1

The area of cloth required to make the conical pandal would be equal to the curved surface area of the cone.

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

It is given that the vertical height ‘h’ = 100 m and base radius ‘r’ = 240 m.

To find the slant height ‘l’ we use the following relation

Slant height, l =

=

=

=

l = 260

Hence the slant height of the given cone is 260 m.

Now, substituting the values of r = 240 m and slant height l = 260 m in the formula for C.S.A,

We get

Curved Surface Area =

=

Hence the area of the cloth required to make the conical pandal would be m²

It is given that the cloth is 100π wide. Now, we can find the length of the cloth required by using the formula,

Length of the canvas required =

=

= 624

Hence the length of the cloth that is required is