Bunuel wrote:

The formula for the volume of a sphere is \(\frac{4}{3}πr^3\). If the radius of a sphere is doubled, the volume of the resulting sphere will be how many times the volume of the original sphere?

A 2

B 4

C 8

D 16

E 32

Scale FactorWhen the volume of figures increases or decreases,

each length is multiplied by a scale factor.

Volume = length * length * length

Each length is doubled. Scale factor is 2.

Scale factor \(k = 2\)

Multiply the original figure by scale factor,

cubed, to calculate change, because

the scale factor changes all three lengths.

\(k^3=2^3=8\)

Answer C

Plug in valuesIf the original radius is 2, and the radius is doubled, then the new radius is 4.

Original volume?

\(\frac{4}{3}πr^3\)

\(\frac{4}{3}π2^3=\)

\(\frac{32}{3}π\)

New volume?

\(\frac{4}{3}πr^3\)

\(\frac{4}{3}π4^3\)

\(\frac{256}{3}π\)

Volume of new sphere is how many times bigger than original sphere?

\(\frac{\frac{256}{3}π}{\frac{32}{3}π}=(\frac{256}{3}π*\frac{3}{32}π)=8\)

Answer C

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