Question

Raymond owns a dairy farm and has to order tanker trucks, which are in the shape of right circular cylinders, to pick up his milk. If the length of each truck is 39 feet, and the diameter is 8.2 feet, how many tanker trucks will Raymond need if he has a volume of 6,175.65 feet3
of milk?(1 point)
Responses

Raymond will need 1 truck since the volume of 1 truck is 8,234.21 feet3
.
Raymond will need 1 truck since the volume of 1 truck is 8,234.21 feet cubed .

Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 feet3
.
Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 feet cubed .

Raymond will need 8 trucks since the volume of 1 truck is 502.09 feet3
.
Raymond will need 8 trucks since the volume of 1 truck is 502.09 feet cubed .

Raymond will need 5 trucks since the volume of 1 truck is 1,004.17 feet3
.

Answer 1

To determine how many tanker trucks Raymond needs, we first need to calculate the volume of one tank truck. The volume \( V \) of a right circular cylinder is given by the formula:

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

where \( r \) is the radius and \( h \) is the height (or length in this case) of the cylinder.

Given:
- The diameter of the truck is 8.2 feet, so the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{8.2}{2} = 4.1 \text{ feet}
\]

- The length \( h \) of the truck is 39 feet.

Now we can plug these values into the volume formula:

\[
V = \pi (4.1)^2 (39)
\]

Calculating \( r^2 \):

\[
(4.1)^2 = 16.81
\]

Now substituting \( r^2 \) back into the volume formula:

\[
V = \pi (16.81)(39) = \pi (655.59)
\]

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

\[
V \approx 3.14159 \times 655.59 \approx 2056.78 \text{ cubic feet}
\]

So, the volume of one truck is approximately 2056.78 cubic feet.

Now we'll determine how many trucks are needed for 6,175.65 cubic feet of milk:

\[
\text{Number of trucks} = \frac{\text{Total volume of milk}}{\text{Volume of one truck}} = \frac{6175.65}{2056.78} \approx 3
\]

Therefore, Raymond will need 3 trucks since the volume of 1 truck is approximately 2056.78 cubic feet.

The correct response is:

**Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 feet³.**