When the radius of a sphere is doubled, what is the resulting change in volume?

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Answer 1 · 2017-05-02T08:05:29

#8# times larger (compared to the original)

The original case: #V=(4/3)*pi*r^3#

Now you have 2r (instead of r)

The new situation: #V'=(4/3)*pi?(2r)^3#

Since the first two terms are identical you can cancel them:

#(V')/V=((2r)^3)/(r^3)#

which will yield:

#(V')/V=(8r^3)/(r^3)#

Finally you will have #(V')/V=8#

In other words, in the new case you will have 8 times larger volume.