Question

The radius and height of a right circular cone are in the ratio $3:4$. If its slant height is $25\text{cm}$, its total surface area is:

• A. $600\pi {\text{cm}}^2$
• B. $225\pi {\text{cm}}^2$
• C. $375\pi {\text{cm}}^2$
• D. $500\pi {\text{cm}}^2$

Answer 1

The correct option is A $600\pi {\text{cm}}^2$

Let $r$ be the radius of the base of the cone, $h$ be its height, and $l$ be its slant height. Then, as per the data:
$r=3x,h=4x$, and by the relation $r^2+h^2=l^2,l=5x$

Given that $l=25\text{cm}$, we have $x=5$
Thus, $r=15\text{cm},h=20\text{cm}$

Hence, its total surface area $=\pi r(l+r)$
$=15\pi \left(40\right)$
$=600\pi {\text{cm}}^2$