Multiple choice

Mr. Raj has a cylinder and a sphere. The sphere is such that it perfectly fits into the cylinder with no part of it being outside. Then, the ratio of curved surface area of the cylinder to the surface area of the sphere will be

  1. 1 : 1

  2. 1 : 2

  3. 2 : 1

  4. 2 : 3

  5. 3 ; 1
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A Correct answer
Explanation

If a sphere fits perfectly in a cylinder, the cylinder height h = 2r and radius = r. Surface area of sphere = 4*pi*r^2. Curved surface area of cylinder = 2*pi*r*h = 2*pi*r*(2r) = 4*pi*r^2. Ratio is 1:1.

AI explanation

Let the radius of the sphere be r, which means the cylinder must have a radius of r and a height of 2r for the sphere to fit perfectly. The curved surface area of the cylinder is found using the formula 2*pi*r*h, which becomes 2*pi*r*(2r) = 4*pi*r^2. The surface area of the sphere is 4*pi*r^2, making the ratio of the curved surface area of the cylinder to the surface area of the sphere 1 to 1.

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