A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other.

Solution:

We have,

the base radius of cone $=$ the base radius of cylinder $=$ the base radius of hemisphere $=r=5 \mathrm{~cm}$,

the height of the cylinder, $H=13 \mathrm{~cm}$,

the total height of the toy $=30 \mathrm{~cm}$

Also, the height of the cone, $h=30-(13+5)=12 \mathrm{~cm}$

The slant heigt of the cone, $l=\sqrt{r^{2}+h^{2}}$

$=\sqrt{5^{2}+12^{2}}$

$=\sqrt{25+144}$

$=\sqrt{169}$

$=13 \mathrm{~cm}$

Now, the surface area of the toy $=$ CSA of cone + CSA of cylinder + CSA of hemisphere

$=\pi r l+2 \pi r H+2 \pi r^{2}$

$=\pi r(l+2 H+2 r)$

$=\frac{22}{7} \times 5 \times(13+2 \times 13+2 \times 5)$

$=\frac{22}{7} \times 5 \times(13+26+10)$

$=\frac{22}{7} \times 5 \times 49$

$=770 \mathrm{~cm}^{2}$

So, the surface area of the toy is $770 \mathrm{~cm}^{2}$.