Question

The height of a conical tent is 14 m and its floor area is 346.5 $m^2$. How much canvas, 1.1 m wide, will be required for it ?

(a) 490 m (b) 525 m (c) 665 m (d) 860 m

Answer 1

Let r= radius of the base.
Given area = 346.5

$\pi \times r^2$ =346.5

$r^2$ = $346.5\times \frac{7}{22}$ = $\frac{441}{4}$

r = $\frac{21}{2}$

l = $\sqrt{r^2+h^2}$=$\sqrt{\frac{441}{4}+{14}^2}$

l = $\frac{35}{2}$ m

The area of canvas = surface area of the cone =$\pi rl$ = $\pi \times \frac{21}{2}\times \frac{35}{2}$ $m^2$ = $\frac{33\times 35}{2}$ $m^2$

Given length of canvas = 1.1 m
Let width = x
Area of canvas = 1.1x
So, 1.1 x=$\frac{33\times 35}{2}$
x=$\frac{33\times 35}{2\times 1.1}$ = 525 m