Question

If the surface are as of two spheres are in the ratio 4 : 9, then find the ratio of their volumes.

Solution

straight S subscript 1 over straight S subscript 2 equals 4 over 9 rightwards double arrow space space space space fraction numerator 4 πr subscript 1 squared over denominator 4 pi r subscript 2 squared end fraction equals 4 over 9 rightwards double arrow space space space space r subscript 1 squared over r subscript 2 squared space equals 4 over 9 rightwards double arrow space space space space r subscript 1 over r subscript 2 equals 2 over 3 therefore space space space space V subscript 1 over V subscript 2 equals fraction numerator 4 over 3 πr subscript 1 cubed over denominator 4 over 3 πr subscript 2 cubed end fraction space space space space space space space space equals space open parentheses r subscript 1 over r subscript 2 close parentheses cubed equals open parentheses 2 over 3 close parentheses cubed equals 8 over 27

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