Question

The radii of the circular ends of the frustum of a right circular cone are $14$ cm and $12$ cm and its thickness is $9$ cm. Find the lateral surface of the frustum. (Take $\pi$ $=3.14$)

• A. $783.6{\text{cm}}^2$
• B. $763.6{\text{cm}}^2$
• C. $753.6{\text{cm}}^2$
• D. $733.6{\text{cm}}^2$

Answer 1

The correct option is C $753.6{\text{cm}}^2$

Curved Surface area of a frustum of a cone $=\pi l(r_1+r_2)$, where $l$ is the slant height

$l=\sqrt{h^2+(r_1-r_2{)}^2}$, where $h$ is the height, $r_1$ and $r_2$ are the radii of the lower and upper ends of a frustum of a cone.

So,

$l=\sqrt{9^2+{(14-12)}^2}$ $=\sqrt{85}\text{cm}$

Hence, Curved Surface area of this frustum of a cone $=3.14\times \sqrt{85}\times (14+12){\text{cm}}^2$

$=753.6{\text{cm}}^2$