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 5 trucks since the volume of 1 truck is 1,004.17 feet3
.
Raymond will need 5 trucks since the volume of 1 truck is 1,004.17 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 3 trucks since the volume of 1 truck is 2,058.55 feet3
.

1 answer

To find out how many tanker trucks Raymond will need, we first need to calculate the volume of one tanker truck, which is in the shape of a right circular cylinder. The formula for the volume \( V \) of a cylinder is:

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

where \( r \) is the radius and \( h \) is the height (or length) of the cylinder. The diameter of the truck is given as 8.2 feet, so the radius \( r \) is half of that:

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

The length (height) of the truck \( h \) is given as 39 feet. Now we can substitute these values into the volume formula:

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

Calculating \( 4.1^2 \):

\[ 4.1^2 = 16.81 \]

Now substituting this into the volume formula:

\[ V \approx \pi \times 16.81 \times 39 \]

Calculating \( 16.81 \times 39 \):

\[ 16.81 \times 39 = 655.59 \]

Now, substituting this back:

\[ V \approx \pi \times 655.59 \approx 2059.29 \text{ feet}^3 \]

(Rounding \( \pi \) to approximately 3.14159 gives the volume)

Now we round this to be specific to the options provided:

\[ V \approx 2058.55 \text{ feet}^3 \text{ (as provided in one of the options)} \]

Now, to determine how many trucks are needed, we divide the total volume of milk by the volume of one truck:

\[ \text{Number of trucks} = \frac{6175.65}{2058.55} \approx 3 \]

So, Raymond will need 3 trucks. The response that states "Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 feet³" is correct.