Question 56

A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?

Solution

Height of cone, $$h$$ = 12 cm and radius of cone, $$r$$ = 5 cm

Radius of hemisphere, $$r$$ = 5 cm

Volume of solid = Volume of cone + Volume of hemisphere

= $$(\frac{1}{3} \pi r^2 h) + (\frac{2}{3} \pi r^3)$$

= $$(\frac{\pi r^2}{3}) [h + 2r]$$

= $$(\frac{22 \times 25}{7 \times 3}) (12 + 10)$$

= $$\frac{22 \times 22 \times 25}{21} = \frac{12100}{21}$$

= $$576.19 cm^2$$

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