Question

The cost of the canvas required to make a conical tent of base radius $8$ m at the rate of Rs. $40$ per $m^2$ is Rs. $10,048$. Find the height of the tent (Take $\pi =3.14)$.

• A. $6$ m
• B. $7$ m
• C. $8$ m
• D. $10$ m

Answer 1

Answer: (A)

$6$ m

To find the amount of canvas required to make a conical tent, we need to calculate the lateral surface area of the tent.

Lateral surface area of a cone of radius $r$, height $h=\pi r\sqrt{h^2+r^2}$.

As the total cost to make the tent is Rs. $10048$ at the rate of Rs. $40$ per $m^2$,

the total area Lateral surface area $=\frac{\text{Total cost of canvas}}{\text{Cost of canvas per}{m}^2}$

$=\frac{10048}{40}=251.2m^2$.

So, lateral surface area:

$\pi r\times \sqrt{h^2+r^2}=251.2$
$\Rightarrow 3.14\times 8\times \sqrt{h^2+8^2}=251.2$
$\Rightarrow \sqrt{h^2+8^2}=10$

Squaring both sides, we get:
$h^2+64=100$
$\Rightarrow h^2=36$
$\Rightarrow h=6m$

Hence, option A is correct.