Multiple choice

The volume of a solid hemisphere is $1152\pi \ cu.cm$. Find its curved surface area.

  1. $288\pi \ {cm}^{2}$
  2. $88\pi\ {cm}^{2}$
  3. $28\pi\ {cm}^{2}$

  4. None of these
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A Correct answer
Explanation

The volume of a hemisphere is (2/3) * pi * r^3 = 1152 * pi. Solving for r^3 gives 1728, so r = 12. The curved surface area is 2 * pi * r^2 = 2 * pi * 144 = 288 * pi.

AI explanation

The volume of a solid hemisphere is (2/3)πr^3, so we set (2/3)πr^3 equal to 1152π. Dividing both sides by π gives (2/3)r^3 = 1152, which means r^3 = 1728 and the radius r is 12 cm. The curved surface area of a hemisphere is 2πr^2, so substituting r = 12 gives an area of 2 x π x 12 x 12 = 288π cm^2. The curved surface area is 288π cm^2.

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