Question

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Answer 1

Radius of cone $=3.5cm,$
Total height of the toy = 15.5cm , height of cone $=15.5–3.5=12$ cm
Slant height of cone can be calculated as follows:
$l=\sqrt{h^2+r^2}$
$=\sqrt{{12}^2+{3.5}^2}$
$=\sqrt{144+12.25}$
$=\sqrt{156.25}=12.5cm$
Curved surface area of cone can be calculated as follows:
$=\pi rl$
$=\frac{22}{7}\times 3.5\times 12.5$
$=137.5c{m}^2$
Curved surface area of hemispherical portion can be calculated as follows:
$=2\pi r^2$
$=2\times \frac{22}{7}\times 3.5\times 3.5$
$=77c{m}^2$
Hence, total surface area =$137.5+77=214.5c{m}^2$