Question:
A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is $16 \mathrm{~cm}$ and its height is $15 \mathrm{~cm}$. Find the cost of painting the toy at Rs. 7 per $100 \mathrm{~cm}$
Solution:
Diameter of cone = 16 cm
Radius of cone = 8 cm
Height of cone = 15 cm
Slant height of cone $=\sqrt{8^{2}+15^{2}}$
$=\sqrt{64+225}$
$=\sqrt{289}=17 \mathrm{~cm}$
Therefore Total curved surface area of toy
$=\pi r l+2 \pi r^{2}$
$=22 / 7 \times 8 \times 17+2 \times 22 / 7 \times 8^{2}$
$=5808 / 7 \mathrm{~cm}^{2}$
Now, cost of $100 \mathrm{~cm}^{2}=$ Rs. 7
$1 \mathrm{~cm}^{2}=$ Rs. $7 / 100$
Hence cost of $5808 / 7 \mathrm{~cm}^{2}=$ Rs. $5808 / 7 \times 7 / 100$
= Rs. 58.08
