Question

A solid is in the form of a hemisphere surmounted by a right circular cone. If height of the cone is $12\text{cm}$ and diameter of the base is $10\text{cm}$. Calculate the surface area of the toy.

Answer 1

Given, Radius, $r$ of cone $=5\text{cm}$
Height, $h$ of cone $=12\text{cm}$

slant height, $l=\sqrt{h^2+r^2}$
$l=\sqrt{{12}^2+5^2}$
$l=\sqrt{144+25}$
$l=\sqrt{169}$
$l=13\text{cm}$

Surface area of the toy = Curve surface area of cone + curved surface area of hemisphere
$=\pi rl+2\pi r^2$
$=\pi r(l+2r)$
$=3.14\times 5(13+2\times 5)$
$=361.1{\text{cm}}^2$