Question

A student said that when you double the radius of a sphere, you double the volume of the sphere. Do you agree or disagree? Give one or more specificexamples to justify your answer.Enter the correct answers in the boxes.Show HintsThe volume of a sphere with a radius of 3 isa7. The volume of a sphere with a radius of 6 isa1. The volume istimes as much.

Answer 1

When calculating the volume, raise the power of the radius to 3. This means that relative to to the radius, its volume will also raise to the power of 3

If we double the radius of the sphere, then

$\begin{gathered} \text{If} \\ r_1=3 \\ r_2=3\cdot2=6 \\ \\ \text{ Volume of Sphere 1} \\ r=3 \\ V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\pi(3)^3 \\ V=\frac{4}{3}\pi(27) \\ V=36\pi \\ \\ \text{Volume of Sphere 2} \\ V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\pi(6)^3 \\ V=\frac{4}{3}\pi(216) \\ V=288\pi \end{gathered}$

Comparing the two volumes

$\frac{288\pi}{36\pi}=8$

Therefore, the volume of the new sphere is 8 times as much.