Question

A sphere is shown below.



A formula for the volume of a sphere is

. The volume of the sphere shown is 800 cubic inches. What is the approximate value of
, the radius of the sphere, in inches?
A.
5.76

B.
14.96

C.
21.87

D.
63.66

Answer 1

The formula for the volume \( V \) of a sphere is given by:

\[
V = \frac{4}{3} \pi r^3
\]

where \( r \) is the radius of the sphere. We are given that the volume of the sphere is 800 cubic inches. We can set up the equation:

\[
\frac{4}{3} \pi r^3 = 800
\]

To solve for \( r \), first multiply both sides by \( \frac{3}{4} \):

\[
\pi r^3 = \frac{3 \times 800}{4}
\]

\[
\pi r^3 = 600
\]

Next, divide both sides by \( \pi \):

\[
r^3 = \frac{600}{\pi}
\]

Now, we can use the approximate value of \( \pi \approx 3.14 \):

\[
r^3 \approx \frac{600}{3.14} \approx 191.08
\]

To find \( r \), we take the cube root:

\[
r \approx \sqrt[3]{191.08}
\]

Calculating the cube root:

\[
r \approx 5.76
\]

Therefore, the approximate value of \( r \), the radius of the sphere, is:

**A. 5.76**