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 π 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 = ` sqrt(r^2 + h^2)`

= ` sqrt( 240^2 + 100^2)`

=  `sqrt( 57600 + 10000)`

=  ` sqrt( 67600)`

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 =  `(pi) (240)(260)`

=  `62400 pi`

Hence the area of the cloth required to make the conical pandal would be `62400  pi`  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 = `("Area of the cloth")/(" Width of the cloth")`

= `(62400 pi)/(1000pi)`

= 624

Hence the length of the cloth that is required is 624 m