Question

A conical tent has a floor area of $154$ sq.m. Its height is$24$m. How much canvas is required for the tent.....

Answer 1

Floor area of conical tent = 154 sq.m.

Height = 24 m

Since, floor of conical tent is circular

So, area of floor = $\pi r^2$

So, $\pi r^2$ = 154

$⟹\frac{22}{7}{r}^2=154$

$⟹r^2$ = $\frac{7}{22}\times 154$

$⟹r^2$ = 49

$⟹r=7$

Also, we know that

$slantheigh{t}^2=heigh{t}^2+radiu{s}^2$

i.e., $l^2=h^2+r^2$

i.e., $l^2={24}^2+7^2$

i.e., $l^2=576+49$

i.e., $l^2=625$

i.e., $l=25$

So, canvas required = curved surface area of the conical tent

= $\pi rl$

= $\frac{22}{7}\times 7\times 25$

= $22\times 25$

= 550 sq.m.