A wooden toy is in the form of a cone surmounted on a hemisphere.

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

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