A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm find the total surface area and volume of the toy.
Radius of hemisphere = 3.5 cm
Total height of the toy = 15.5 cm.
Surface area of cone
$=\pi r l$
$I=\sqrt{(12)^{2}+(3.5)^{2}}$
$=\sqrt{156.25}$
$=12.5 \mathrm{~cm}$
Therefore,
Surface area of cone
$=\frac{22}{7} \times 3.5 \times 12.5$
$=137.5 \mathrm{~cm}^{2}$
Surface area of hemisphere
$=2 \pi r^{2}$
$=77 \mathrm{~cm}^{2}$
Therefore,
Total surface area of the toy
$=137.5+77$
$=214.5 \mathrm{~cm}^{2}$'
Volume of cone
$=\frac{1}{3} \pi r^{2} h$
$=154 \mathrm{~cm}^{2}$
Volume of hemisphere
$=\frac{2}{3} \pi r^{3}$
$=\frac{2}{3} \times \frac{22}{7} \times(3.5)^{3}$
$=89.83 \mathrm{~cm}^{3}$
Therefore,
Total volume of the toy
$=(154+89.83) \mathrm{cm}^{3}$
$=243.83 \mathrm{~cm}^{3}$