Question

The volume of a sphere, V, with radius r can be determined using the formula V equals four-thirds pi r cubed, where pi is approximately 3.14.



What is the approximate volume of a sphere with a ,begin emphasis,diameter,end emphasis,​ of 12 meters?

Answer options with 4 options
A.
100.5 meters cubed

B.
150.7 meters cubed

C.
904.3 meters cubed

D.
7234.6 meters cubed

Answer 1

To find the volume of a sphere with a diameter of 12 meters, we first need to determine the radius. The radius \( r \) is half of the diameter:

\[
r = \frac{diameter}{2} = \frac{12 \text{ meters}}{2} = 6 \text{ meters}
\]

Next, we can use the formula for the volume of a sphere:

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

Substituting \( r = 6 \text{ meters} \) and \( \pi \approx 3.14 \):

\[
V = \frac{4}{3} \times 3.14 \times (6^3)
\]

Calculating \( 6^3 \):

\[
6^3 = 216
\]

Now substituting this value back into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 216
\]

Calculating \( \frac{4}{3} \times 3.14 \):

\[
\frac{4}{3} \times 3.14 \approx 4.1867
\]

Now multiplying by 216:

\[
V \approx 4.1867 \times 216 \approx 904.3 \text{ meters cubed}
\]

Thus, the approximate volume of the sphere is:

\[
\boxed{904.3 \text{ meters cubed}}
\]

The correct answer is C. 904.3 meters cubed.