Multiple choice

The ratio of the radius of two sphere is 3 : 2 Then the ratio of their surface area is

  1. $4 : 9$
  2. $3 : 2$
  3. $\displaystyle \sqrt{3}:\sqrt{2}$
  4. $9 : 4$
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D Correct answer
Explanation

The surface area of a sphere is proportional to the square of its radius (A = 4*pi*r^2). If the ratio of radii is 3:2, the ratio of surface areas is 3^2 : 2^2 = 9:4.

AI explanation

The surface area of a sphere is given by the formula 4 * pi * r^2, meaning the area is proportional to the square of the radius. Therefore, the ratio of their surface areas is the square of the ratio of their radii, which is 3^2 : 2^2. This calculates to 9 : 4.

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