Multiple choice

Both the radius and the height of a cylinder are individually equal to the radius of a sphere. What would be the volume of a hemisphere cut out of this sphere, if the volume of the cylinder is 144 cm3?

  1. 96 cm3

  2. 48 cm3

  3. 192 cm3

  4. 128 cm3

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cylinder volume = pi * r^2 * h = 144. Since r = h = radius of sphere (R), pi * R^3 = 144. Hemisphere volume = 2/3 * pi * R^3. Substituting pi * R^3 = 144, volume = 2/3 * 144 = 96.

AI explanation

Let the radius of the sphere be r; then the radius and height of the cylinder are also r. The volume of the cylinder is pi*r^2*h = pi*r^2*r = pi*r^3 = 144 cm3. The volume of a hemisphere of radius r is given by the formula (2/3)*pi*r^3. Substituting pi*r^3 = 144 gives (2/3) * 144 = 96 cm3. The result is 96 cm3.

Keep practicing — related questions