Question

A cloth having an arca of 165$m^2$ is shapedinto the form of a conical text of radius 5 $m$ .
How many students can sit in the tent, ifa student on an average occupies $\frac{5}{7}{m}^2$on the ground?
(ii) Find the volume of the cone.

Answer 1

(i) Number of students who can sit in the tent if a student, on an average, occupies $\frac{5}{7}{m}^2$ on the ground.

$=\frac{\frac{\pi r^2}{5}}{7}=\frac{22}{7}\times (5{)}^2\times \frac{7}{5}=110$

(ii) Area of cloth $=165m^2$

Curved surface area of conical tent $=\pi rl$

$\therefore \pi rl=165$

$\Rightarrow l=\frac{165}{\pi r}=\frac{165}{\frac{22}{7}\times 5}=\frac{165\times 7}{22\times 5}=\frac{21}{2}m$

Now, $l^2=r^2+h^2$

$\Rightarrow h=\sqrt{l^2-r^2}$

$=\sqrt{{\left(\frac{21}{2}\right)}^2-(5{)}^2}$

$\Rightarrow h=\sqrt{\frac{441}{4}-25}=\frac{\sqrt{341}}{2}$

$=\frac{1}{2}\times 18.47=9.24m$ (approx)

Volume of conical tent $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times (5{)}^2\times 9.24$

$=\frac{550\times 9.24}{21}=\frac{5082}{21}=242m^3$