A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total
surface area of the toy.
We have,
Radius of the hemisphere $=$ Radius of the cone $=r=3.5 \mathrm{~cm}$ and
Height of the cone $=15.5-3.5=12 \mathrm{~cm}$
Also,
The slant height of the cone, $l=\sqrt{h^{2}+r^{2}}$
$=\sqrt{12^{2}+3.5^{2}}$
$=\sqrt{144+12.25}$
$=\sqrt{156.25}$
$=12.5 \mathrm{~cm}$
Now,
Total surface area of the toy $=$ CSA of cone $+$ CSA of hemisphere
$=\pi r l+2 \pi r^{2}$
$=\pi r(l+2 r)$
$=\frac{22}{7} \times 3.5 \times(12.5+2 \times 3.5)$
$=11 \times(12.5+7)$
$=11 \times 19.5$
$=214.5 \mathrm{~cm}^{2}$
So, the total surface area of the toy is 214.5 cm2.
Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.