Question

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. [Use π = 3.14]

Answer 1

Height (h) of conical tent = 8 m

Radius (r) of base of tent = 6 m

Slant height (l) of tent = `sqrt(r^2+h^2)`

= `sqrt(6^2+8^2)  m`

= `sqrt100  m`

= 10 m

The curved surface area of conical tent = πrl

= (3.14 × 6 × 10) m²

= `314/100 xx 6 xx 10  m^2`

= 188.4 m²

Let the length of the tarpaulin sheet required be l.

As 20 cm will be wasted, therefore, the effective length will be (l − 0.2 m).

Breadth of tarpaulin = 3 m

Area of sheet = Curved surface area of the tent

[(l − 0.2 m) × 3] m = 188.4 m²

l − 0.2 m = 62.8 m

l = 63 m

Therefore, the length of the required tarpaulin sheet will be 63 m.