Question

If the diameter of a right cone is $6cm$ and its vertical height is $4cm$, then its curved surface area is:

• A. $47.1$ $c{m}^2$
• B. $48$ $c{m}^2$
• C. $49$ $c{m}^2$
• D. $50$ $c{m}^2$

Answer 1

Answer: (A)

The correct option is A $47.1$ $c{m}^2$
Given, the vertical height is $h=4cm$

and diameter is $d=6cm$.

Then, radius $=\frac{d}{2}=\frac{6}{2}=3cm$.

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

$=\sqrt{(3{)}^2+(4{)}^2}=\sqrt{9+16}$

$=\sqrt{25}=5cm$.

Then, the curved surface area of a right circular cone

$=\pi rL$

$=\pi \times 3\times 5$

$=3.14\times 5\times 3$

$=47.1c{m}^2$.

Hence, option $A$ is correct.