Question

The volume of a right cone is 924$m^2$ and its height is 18 m then lateral surface area is

• A. $22\sqrt{115}{m}^2$
• B. $310m^2$
• C. $22\sqrt{373}{m}^2$
• D. $276m^2$

Answer 1

The correct option is C $22\sqrt{373}{m}^2$

Volume of a cone $=\frac{1}{3}\pi r^{2}h$ where r is the
radius of the base of the cone and h is the height.
Hence, $ \frac { 1 }{ 3 }\frac { 22 }{ 7 } \times { r }^{ 2 }\times 18 = 924 { r }^{ 2 }
= 49 r = 7 m $

For a cone, l $=\sqrt{h^2+r^2}$ where l is the slant height.

Hence, $l=\sqrt{{18}^2+7^2}$

$l=\sqrt{373}$

Hence,
CSA of this cone, $=\frac{22}{7}\times 7\times \sqrt{373}=22\sqrt{373}sqm$