Multiple choice

The curved surface areas of a right circular cylinder and a sphere are equal. Also, the radii of the cylinder and sphere are equal. Then the ratio of their volume will be?

  1. $2 : 3$
  2. $3 : 2$
  3. $3 : 4$
  4. $4 : 3$
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B Correct answer
Explanation

Cylinder CSA = 2*pi*r*h. Sphere CSA = 4*pi*r^2. Given 2*pi*r*h = 4*pi*r^2, we find h = 2r. Ratio of volumes = (pi*r^2*h) / (4/3*pi*r^3) = (pi*r^2*2r) / (4/3*pi*r^3) = 2 / (4/3) = 6/4 = 3:2.

AI explanation

Let r be the common radius and h be the height of the cylinder. Equating the curved surface areas gives 2 * pi * r * h = 4 * pi * r^2, so h = 2 * r. The ratio of the volume of the cylinder to the volume of the sphere is (pi * r^2 * h) / ((4/3) * pi * r^3). Substituting h = 2 * r gives 2 / (4/3), which simplifies to 3 : 2.

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