Question

A tent is in the form of a cylinder of diameter $15m$ and height $2.4m$, surmounted by a cone of same base and height $4m$. Find the cost of the canvas at Rs. $50$ per square meter. (Take $\pi$ = $\frac{22}{7}$)

• A. $Rs.15765$
• B. $Rs.15875$
• C. $Rs.15775$
• D. $Rs.15675$

Answer 1

The correct option is D $Rs.15675$

Diameter of cylinder$=15m$

$\therefore$Radius of cylinder$=\frac{15}{2}=7.5m$

Height $h_1=2.4m$

Height of cone, $h_2=4m$

Capacity of cone$=\pi r^2{h}_1+\frac{1}{3}\pi r^2{h}_2$

$=\pi r^2(h_1+\frac{h_2}{3})$

$=\frac{22}{7}\times {\left(7.5\right)}^2(2.4+\frac{4}{3})$

$=\frac{4620}{7}=660m^2$

Slant height of cone$=\sqrt{r^2+h_2^2}=\sqrt{{\left(7.5\right)}^2+{\left(4\right)}^2}=8.5m$

CSA of cone$=\pi rl=\frac{22}{7}\times 7.5\times 8.5$

$=200.35m^2$

CSA of cylindrical part$=2\pi rh=2\times \frac{22}{7}\times 7.5\times 2.4$

$=113.14m^2$

Total CSA of tent$=200.35+113.14=313.49m^2$

Therefore cost of canvas$=313.49\times 50=$Rs. $15674.5$