Question

A cylindrical diesel fuel holding tank has a radius of 6 feet and a length of 12 feet. What is the maximum volume of fuel the tank can hold? (to nearest whole number)
Responses
A 339
339 ft 3
B 679
679 ft 3
C 1,357
1,357 ft 3
D 2,714

Answer 1

To find the maximum volume of a cylindrical tank, we use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

where:
- \( V \) is the volume,
- \( r \) is the radius, and
- \( h \) is the height (or length in the case of a horizontal cylinder).

Given:
- The radius \( r = 6 \) feet
- The length \( h = 12 \) feet

Substituting the values into the formula:

\[
V = \pi (6)^2 (12)
\]

Calculating \( (6)^2 \):

\[
(6)^2 = 36
\]

Now substituting this back into the volume formula:

\[
V = \pi (36) (12)
\]

Calculating \( 36 \times 12 \):

\[
36 \times 12 = 432
\]

Now substituting this back:

\[
V = \pi \times 432
\]

Now using \( \pi \approx 3.14159 \):

\[
V \approx 3.14159 \times 432 \approx 1357.44
\]

Rounding this to the nearest whole number gives:

\[
V \approx 1357
\]

Therefore, the maximum volume of fuel the tank can hold is:

\[
\boxed{1357} \text{ ft}^3
\]

Thus the correct response is **C: 1,357** ft³.