What percentage increase in the radius of a sphere will c...
What percentage increase in the radius of a sphere will cause its volume to increase by 45%?
13%
15%
23%
25%
Correct answer is A
Let the original volume be V with radius r.
V=43πr3
45% increased volume = 145%V.
Let the %age increase in radius = m%r
145100V=43π(mr100)3
1.45V=(43πr3)(m100)3
1.45V=V(m100)3
⟹1.45×106=m3
m=3√1.45×106=113.2
∴
\approxeq 13%
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