Multiple choice

A hemispherical bowl of radius unity is filled up with water upto the depth $\cfrac { 1 }{ 2 } $. The volume of water in the bowl is

  1. $\cfrac { 27\pi }{ 24 } $
  2. $\cfrac { 5\pi }{ 24 } $
  3. $\cfrac { 3\pi }{ 4 } $

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of a spherical cap is (pi * h^2 / 3) * (3R - h). Here R=1, h=1/2. V = (pi * (1/4) / 3) * (3 - 1/2) = (pi / 12) * (5/2) = 5 * pi / 24.

AI explanation

Using the formula for the volume of a spherical cap, V = (πh^2 / 3)(3R - h), we substitute R = 1 and h = 1/2. This gives V = (π(1/2)^2 / 3)(3(1) - 1/2) = (π/12)(5/2). Multiplying these fractions yields a volume of 5π/24.

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