Question

A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is $21cm$ and its volume is $\frac{2}{3}$ of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy. (Use $\pi =22/7$)

Answer 1

Volume of cone =$\frac{2}{3}$ Volume of hemisphere

$\frac{1}{3}\pi r^{2}h=\frac{2}{3}\left(\frac{2}{3}\pi r^3\right)$ ; r =Common radius h = Cone height

$h=\frac{4}{3}r=\frac{4}{3}\left(21\right)=28cm$

Slant height, $l=\sqrt{r^2+h^2}=\sqrt{{21}^2+{28}^2}=35cm$

Total surface area = $CS{A}_{cone}+CS{A}_{hemisphere}$

$=\pi rl+2\pi r^2=\pi r(l+2r)=5082c{m}^2$