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 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 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 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 .
Answers
GPT-4o mini
To determine how many tanker trucks Raymond will need, we first need to calculate the volume of one cylindrical tanker truck.
The volume \( V \) of a right circular cylinder can be calculated using the formula:
\[
V = \pi r^2 h
\]
Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (or length) of the cylinder.
Given:
- The diameter of the truck = 8.2 feet, so the radius \( r \) = 8.2 / 2 = 4.1 feet,
- The length \( h \) = 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 substitute back into the volume formula:
\[
V = \pi (16.81)(39)
\]
Calculating the multiplication:
\[
16.81 \times 39 = 655.59
\]
Now we multiply by \( \pi \):
\[
V \approx 3.14159 \times 655.59 \approx 2058.55 \text{ feet}^3
\]
Now that we have the volume of one truck, we need to determine how many trucks are needed to transport a total volume of 6,175.65 feet³ of milk:
\[
\text{Number of trucks} = \frac{\text{Total volume of milk}}{\text{Volume of one truck}} = \frac{6175.65}{2058.55} \approx 3
\]
Since we cannot have a fraction of a truck, we round up if necessary. But since 3 is a whole number in this case, he would just need 3 trucks.
Therefore, the correct response is:
**Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 feet³.**
The volume \( V \) of a right circular cylinder can be calculated using the formula:
\[
V = \pi r^2 h
\]
Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (or length) of the cylinder.
Given:
- The diameter of the truck = 8.2 feet, so the radius \( r \) = 8.2 / 2 = 4.1 feet,
- The length \( h \) = 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 substitute back into the volume formula:
\[
V = \pi (16.81)(39)
\]
Calculating the multiplication:
\[
16.81 \times 39 = 655.59
\]
Now we multiply by \( \pi \):
\[
V \approx 3.14159 \times 655.59 \approx 2058.55 \text{ feet}^3
\]
Now that we have the volume of one truck, we need to determine how many trucks are needed to transport a total volume of 6,175.65 feet³ of milk:
\[
\text{Number of trucks} = \frac{\text{Total volume of milk}}{\text{Volume of one truck}} = \frac{6175.65}{2058.55} \approx 3
\]
Since we cannot have a fraction of a truck, we round up if necessary. But since 3 is a whole number in this case, he would just need 3 trucks.
Therefore, the correct response is:
**Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 feet³.**