Multiple choice

A sphere and the base of a cylinder have equal radii. The diameter of the sphere is equal to the height of the cylinder. The ratio of the curved surface area of the cylinder and surface area of the sphere is .....

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

Let radius of sphere = r. Height of cylinder = 2r. Curved surface area of cylinder = 2 * pi * r * h = 2 * pi * r * (2r) = 4 * pi * r^2. Surface area of sphere = 4 * pi * r^2. The ratio is 1:1.

AI explanation

Let the radius of the sphere be r, meaning its surface area is 4πr^2. The diameter of the sphere is 2r, which equals the height of the cylinder, so the curved surface area of the cylinder is 2πr(2r) = 4πr^2. The ratio of the curved surface area of the cylinder to the surface area of the sphere is 4πr^2 : 4πr^2, which simplifies to 1:1.

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