Question 92

A cone of height 25 cm and diameter 21 cm is mounted on a hemisphere of the same diameter. Find the volume of the solid thus formed? (Take π = 22/7)

Solution

Height of cone, $$h$$ = 25 cm and radius of cone, $$r$$ = 10.5 cm

Radius of hemisphere, $$r$$ = 10.5 cm

Volume of solid = Volume of cone + Volume of hemisphere

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

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

= $$(\frac{22 \times (10.5)^2}{7 \times 3}) (25 + 21)$$

= $$22 \times 5.25 \times 46$$

= $$5313$$ $$cm^2$$

=> Ans - (D)

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