Question

A toy is in the form of a cone mounted on a hemisphere of radius $3.5cm$. The total height of the toy is $15.5cm$, find the total surface area and volume of the toy.

Answer 1

TSA of toy$=\pi rl+2\pi r^2=\pi r(\sqrt{r^2+h^2}+2r)$

$=\frac{22}{7}\times 3.5(\sqrt{{3.5}^2+{12}^2}+2\times 3.5)$

$=214.5c{m}^2$

Volume of toy$=\frac{1}{3}\pi r^{2}h=\frac{2}{3}\pi r^3=\frac{1}{3}\pi r^2[h+2r]$

$=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5(12+2\times 3.5)=243.83c{m}^3$