Question

A toy is in the shape of a cone surmounting a hemisphere of radius 21 cm if the height of the cone is 28 cm, the total surface area of the toy is

• A. $4824c{m}^2$
• B. $4076c{m}^2$
• C. $5082c{m}^2$
• D. None

Answer 1

The correct option is C $5082c{m}^2$

Surface area of the toy $=$ Curved surface area of hemispherical part $+$ Curved surface area if 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 of the conical part $=21cm$

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

Hence, l $ = \sqrt { { 28 }^{2 }+ {21}^{ 2 } } $

$l=35cm$

Curved Surface Area of a hemisphere of radius 'r' $=2\pi r^2$
Hence, surface area of the toy $ = (2\pi \times {21}^{2}) + (\pi \times 21 \times 35) = 1617\pi = 5082 {cm}^{2} $