Question

The radius of a right circular cone is $3$ cm and its height is $4$ cm. The total surface area of the cone is:

• A. $48.4$ sq. cm
• B. $64.4$ sq.cm
• C. $96.44$ sq.cm
• D. $75.4$ sq.cm

Answer 1

Answer: (D)

$75.4$ sq.cm

Given, radius $r=3cm$

and height $h=4cm$

Then, slant height $l=\sqrt{r^2+h^2}$

$\Rightarrow l=\sqrt{3^2+4^2}$

$=\sqrt{9+16}$

$=\sqrt{25}=5cm$

Total surface area of a cone $=\pi rl+\pi r^2$

$=\pi \left(3\right)\left(5\right)+\pi (3{)}^2$

$=15\pi +9\pi$

$=24\pi =24\times 3.14$

$=75.36c{m}^2\approx 75.4c{m}^2$

Therefore, option $D$ is correct.