Answer to Question #254 in Geometry for Donna

Question

Surface squares of two spheres refer as m:n. How do their volumes refer?

Answer 1

Surface square of a sphere can be expressed by the formula: S = 4*π*R². The volume of the sphere can be expressed by the formula: V = 4*π*R³/3. Let's consider that radiuses of two spheres are R1 and R2. In this case S1/S2 = (4*π*R1²)/( 4*π*R2²) = (R1²)/( R2²) = m/n => R1/R2 = sqrt (m/n). V1/V2 =
= (4*π*R1³/3)/( 4*π*R2³/3) = (R1³)/( R2³) = (m/n)^(3/2).