Question

What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material will be required for stitching margins and wastage in cutting is approximately 20 cm (Use $\mathrm{\pi }$ = 3.14)

Answer 1

The total amount of canvas required 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 base radius r = 6 m and vertical height h = 8 m.

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

Slant height,

l =

=

=

=

l = 10 m

Now, substituting the values of r = 6 m and slant height l = 10 m and using π = 3.14 in the formula of C.S.A,

We get Curved Surface Area =

= 188.4

Hence the curved surface area of the cone is 188.4 m²

Now, the width of the canvas is 3 m.

Area of the canvas required = (Width of the canvas) (Length of the canvas)

Therefore,

Length of the canvas =

=

= 62.8

Length of canvas is 62.8 m. But we need to add another 20 cm of length for wastage.

20 cm = 0.2 m.

Hence the total amount of canvas length required is