Question 94
By what percentage should the radius of a sphere be increased so that the volume increases by 200%?
Solution
Volume increases by 200% means the volume must becomes 3 times the original one
Hence, V2 = 3*V1
(4/3)*(22/7)*(R2)*(R2)*(R2) = 3*(4/3)*(22/7)*(R1)*(R1)*(R1)
R2 = $$\sqrt[\ 3]{3}$$ * R1
Hence, percentage increase = ({[$$\sqrt[\ 3]{3}$$ * R1] - R1}/R1)*100 = $$\left(\sqrt[\ 3]{3}-\ 1\right)\cdot100$$
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