If the volume of a sphere is increased by 1525/16% without changing the shape then by how much percentage will the surface area of the sphere increase?(Ans:144.14%)

Asked by Rachael Therese | 26th Oct, 2012, 07:55: AM

Expert Answer:

1525/16% = 0.953125
Volume of sphere = (4/3)*pi*r^3

Thus a sphere whose volume increases from V to 1.953125*V has a radius which increases by a factor (1.953125)^(1/3) = 1.25

Surface area of a sphere = 4*pi*r^2

A sphere whose radius increases by a factor of 1.25 has an area increase of 1.25^2 = 1.5625

That's an increase of 56.25%.

Answered by  | 28th Oct, 2012, 11:02: PM

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