Question

The sphere is _____ cubic centimeters bigger than the cube. (Round to the nearest cubic centimeter.)

Answer 1

ANSWER

The sphere is 10762 cubic centimeters bigger than the cube.

EXPLANATION

We want to find the difference in the volumes of the sphere and the cube.

To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.

The volume of a sphere is given as:

$V=\frac{4}{3}\pi r^3$

where r = radius

The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:

$\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot15^3 \\ V\approx14137\operatorname{cm}^3 \end{gathered}$

The volume of a cube is given as:

$V=s^3$

where s = length of the side

The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:

$\begin{gathered} V=15^3 \\ V=3375\operatorname{cm}^3 \end{gathered}$

Therefore, the difference in the volumes of the sphere and cube is:

$\begin{gathered} V_d=V_s-V_c \\ V_d=14137-3375 \\ V_d=10762\operatorname{cm}^3 \end{gathered}$

Therefore, the sphere is 10762 cubic centimeters bigger than the cube.