Question

The total surface area of a cone is $71.28$ c$m^2$. Find the volume of this cone if the diameter of the base is $5.6$ cm.

• A. $29.19$ c$m^3$
• B. $42.12$ c$m^3$
• C. $37.33$ c$m^3$
• D. $36.96$ c$m^3$

Answer 1

Answer: (D)

Total surface area of a cone $71.28c{m}^2$
Diameter of the base $=5.6$ cm
$\therefore$ radius $=2.8$ cm
Surface area of a cone $A=\pi r(r+\sqrt{h^2+r^2})$
$\Rightarrow 71.28=\pi 2.8(2.8+\sqrt{h^2+{2.8}^2})$
$\Rightarrow h=4.5$ cm
Volume of a cone $V=\frac{1}{3}\pi r^{2}h$
$\Rightarrow V=\frac{1}{3}\times \frac{22}{7}\times {2.8}^2\times 4.5$
$\Rightarrow V=36.96c{m}^3$