Question

A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. The surface area of the toy is :

• A. $36\pi c{m}^2$
• B. $33\pi c{m}^2$
• C. $35\pi c{m}^2$
• D. $24\pi c{m}^2$

Answer 1

The correct option is B $33\pi c{m}^2$

Surface area of the toy $=$ Curved surface area of hemispherical part $+$ Curved surface area of the conical part.
Curved surface area of a cone $=\pi rl$ where $r$ is the radius of the cone and $l$ is the slant height.

Radius(r) of the conical part $=\frac{Diameter}{2}=3cm$

Height of the conical part $=4$ cm

For a cone, $l=\sqrt{h^2+r^2}$ where $h$ is the height.

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

$l=5$ cm
Radius of the hemispherical part $=\frac{Diameter}{2}=3cm$
Curved surface area of a hemisphere of radius 'r' $=2\pi r^2=18\pi c{m}^2$

Hence, surface area of the toy $=\left(18\pi \right)+\left(15\pi \right)=33\pi {cm}^2$