Question

A conical tent of radius of $12\text{m}$ and height $16\text{m}$ is to be made, then the cost of canvas required at the rate $\text{Rs.}10$ per ${\text{m}}^2$ is:

• A. $\text{Rs.}7445$
• B. $\text{Rs.}7543$
• C. $\text{Rs.}7550$
• D. $\text{Rs.}7500$

Answer 1

The correct option is B $\text{Rs.}7543$

Given the radius, $r$ and height, $h$ of tent is $12\text{m}$ and $16\text{m}$ respectively.

Then, slant height of tent, $l=\sqrt{r^2+h^2}=\sqrt{(12{)}^2+(16{)}^2}=\sqrt{144+256}=\sqrt{400}=20\text{m}$

Now, curved surface area of tent $=\pi rl=3.143\times 12\times 20{\text{m}}^2=754.30{\text{m}}^2$.

Cost of $1\text{m}$ canvas = $Rs.10$

Total cost of canvas required$=\text{Rs.}754.30\times 10=\text{Rs.}7543$.

Hence, option $B$ is correct.