Multiple choice

Area of base of a solid hemisphere is 36 $\pi $ sq cm. Then its volume is :

  1. $288 \pi cm^{3}$
  2. $108 \pi cm^{3}$
  3. $144 \pi cm^{3}$
  4. $72 \pi cm^{3}$
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C Correct answer
Explanation

Area of base of hemisphere = pi * r^2 = 36 * pi. r^2 = 36, r = 6. Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * 216 = 144 * pi.

AI explanation

The area of the circular base is pi * r^2, so setting pi * r^2 = 36 * pi gives a radius of 6 cm. The volume of a solid hemisphere is two-thirds the volume of a full sphere, given by the formula (2/3) * pi * r^3. Substituting r = 6 yields (2/3) * pi * (216), which calculates to 144 * pi cubic cm.

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