Question

Radius and slant height of a solid right circular cone are in the ratio $3:5$. If the curved surface area is $60\pi sq.cm$, then find its total surface area.

• A. $301\frac{5}{7}{cm}^2$
• B. $31\frac{5}{7}{cm}^2$
• C. $302\frac{5}{7}{cm}^2$
• D. None of these

Answer 1

The correct option is A $301\frac{5}{7}{cm}^2$

We have,

$r:l=3:5$

$\frac{r}{l}=\frac{3}{5}$

$r=\frac{3l}{5}$ $........\left(1\right)$

Curved surface area $=60\pi c{m}^2$

We know that the curved surface area of the cone

$=\pi rl$

So,

$\pi rl=60\pi$

$rl=60$

$\frac{3l^2}{5}=60$ From equation $\left(1\right)$

$l^2=100$

$l=10cm$

So, $r=6cm$

We know that the total surface area

$=\pi r(r+l)$

So,

$=\frac{22}{7}\times 6(6+10)$

$=\frac{22}{7}\times 6\times 16$

$=\frac{2112}{7}=301\frac{5}{7}c{m}^2$

Hence, this is the answer