Directions : Answer the question independently. Suppose r1 is the radius of the sphere with volume numerically equal to the total surface area of a hemisphere with radius equal to r1. Similarly r2 is the radius of the sphere with volume numerically equal to its curved surface area. The ratio r1 : r2 is equal to:

Using the sphere volume formula of 4/3 * pi * r^3 and hemisphere surface area formula of 3 * pi * r^2, we equate them for r1 as 4/3 * pi * r1^3 = 3 * pi * r1^2 to find r1 = 9/4. Similarly, equating the sphere's volume to its curved surface area gives 4/3 * pi * r2^3 = 4 * pi * r2^2, yielding r2 = 3. The ratio r1 : r2 becomes 9/4 : 3, which simplifies to 3:4.

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