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]

#### Solution

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 = 10m`

CSA of conical tent = π*rl*

= (3.14 × 6 × 10) m^{2}

= 188.4 m^{2}

Let the length of 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 = CSA of tent

[(*l* − 0.2 m) × 3] m = 188.4 m^{2}

*l* − 0.2 m = 62.8 m

*l* = 63 m

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