Question

Question 3 (ii)
A cloth having an area of $165m^2$ is shaped into the form of a conical tent of radius 5 m.

(i) Find the volume of the cone.

Answer 1

Given, area of the cloth to form conical tent $=165m^2$
Radius of the base of conical tent, r = 5 m
Curved surface area of conical tent = Area of cloth to form a conical tent
$\Rightarrow \pi rl=165m^2$
$\Rightarrow \frac{22}{7}\times 5\times l=165$
$\therefore l=\frac{165\times 7}{22\times 5}=\frac{33\times 7}{22}=10.5m$
Now,height of the conical tent $=\sqrt{l^2-r^2}=\sqrt{(10.5{)}^2-(5{)}^2}$
$=\sqrt{110.25-25}=\sqrt{85.25}=9.23m$
Volume of the cone (conical tent) $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 5\times 5\times 9.23$
$=\frac{1}{3}\times \frac{1550\times 9.23}{7}=\frac{5076.5}{7\times 3}=241.7m^3$
Hence, the volume of the cone (conical tent) is $241.7m^3$.