Question

A toy made from a hemisphere, a cylinder and a cone is as shown in the figure. Find the total area of the toy..

Answer 1

Given that,

Height of cylinder $=40cm=h$

Radius of cone, hemisphere $=3cm=r$

Height of cone $=40cm=h$

Total surface area of toy = curved surface area of hemisphere + curved surface area of cylinder + curved surface area of cone.

We know that,

CSA of hemisphere $=2\pi r^2$

CSA of cylinder $=2\pi rh$

and CSA of cone $=\pi rl$

Where, $l$ is the slant height of the cone, which is $\sqrt{r^2+h^2}$

$\therefore l^2=r^2+h^2=3^2+4^2=9+16=25$

$l^2=25\Rightarrow l=\sqrt{25}=5cm$

Curved surface area of hemisphere $=2\pi r^2$

$=2\times \frac{22}{7}\times 3^2$

$=56.57c{m}^2$

Curved surface area of cylinder $=2\pi rh$

$=2\left(\frac{22}{7}\right)\times 3\times 40$

$=754.28c{m}^2$

Curved surface area of cone $=\pi rl$

$=\frac{22}{7}\times 3\times 5$

$=47.14c{m}^2$

$\therefore$ Total surface area of the toy $=2\pi r^2+2\pi rh+\pi rl$

$\Rightarrow 56.57c{m}^2+754.28c{m}^2+47.14c{m}^2$

$=(56.57+47.14+754.28)c{m}^2$

$=857.99c{m}^2$

Hence, the total surface area of the toy is $857.99c{m}^2$.