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In the figure, a solid consists of a hemisphere surmounted by a right circular cone,...

Mathematics
JAMB 1988

In the figure, a solid consists of a hemisphere surmounted by a right circular cone, with radius 3.0cm and height 6.0cm. Find the volume of the solid

  • A. 36\(\pi\)cm 3
  • B. 54\(\pi\)cm 2
  • C. 18\(\pi\)cm 2
  • D. 108\(\pi\)cm 2
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Correct Answer: Option A
Explanation

The volume of the solid = vol. of cone + vol. of hemisphere

volume of cone = \(\frac{1}{3} \pi r^2 h\)

= \(\frac{1 \pi}{3} \times (3)^2 x 6 = 18 \pi cm^2\)

vol. of hemisphere = \(\frac{4 \pi r^3}{6} = \frac{2 \pi r^3}{3}\)

= \(\frac{2 \pi}{3} \times (3)^3 = 18\pi cm^3\)

vol. of solid = 18\(\pi\) + 18\(\pi\)

= 36\(\pi\)cm3


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