Question

Monica has a piece of Canvas whose area is 551 m². She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and wastage incurred while cutting, amounts to approximately 1 m². Find the volume of the tent that can be made with it.

Answer 1

Given that out of the 551 m², 1 m² has to be used for stitching, etc we are left with 550 m² of canvas to make a tent.

The amount of canvas needed to make the conical tent would be equal to the curved surface area of the conical tent.

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

Here the C.S.A = 550 m² and the base radius ‘r’ = 7 m. We can get the slant height ‘l’ of the tent by using the formula for curved surface area.

l =

=

= 25

Hence the slant height of the conical tent is 25 m.

The height ‘h’ can be found out using the relation between r, l and h.

We know that in a cone

=

=

=

= 24

Hence the height of the conical tent is 24 m.

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

Volume of cone =

Substituting the values of r = 7 m and h = 24 m in the above equation and using we get,

Volume =

= (22) (7) (8)

= 1232

Hence the volume of the conical tent that can be made out of the given canvas with the given dimensions is