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 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
.
Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 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 .
of milk?(1 point)
Responses
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
.
Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 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 needs, we first need to calculate the volume of one tanker truck.
The volume \( V \) of a right circular cylinder is given by the formula:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the base,
- \( h \) is the height (or length) 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 of the truck \( h \) is 39 feet.
Now we can plug these values into the volume formula:
\[
V = \pi (4.1)^2 (39)
\]
Calculating \( (4.1)^2 \):
\[
(4.1)^2 = 16.81
\]
Now, substituting this value into the volume formula:
\[
V = \pi (16.81)(39)
\]
Calculating \( 16.81 \times 39 \):
\[
16.81 \times 39 = 656.19
\]
Now, multiplying by \( \pi \) (approximately 3.14159):
\[
V \approx 3.14159 \times 656.19 \approx 2068.58 \text{ cubic feet}
\]
Now that we have the volume of one truck, we can find out how many trucks are needed for 6,175.65 cubic feet of milk:
\[
\text{Number of trucks} = \frac{\text{Total volume of milk}}{\text{Volume of one truck}} = \frac{6175.65}{2068.58} \approx 2.99
\]
Since Raymond cannot order a fraction of a truck, he will need to round up to the nearest whole number. Therefore, he will need **3 trucks**.
Thus, the correct response is:
**Raymond will need 3 trucks since the volume of 1 truck is approximately 2068.58 feet³.**
The volume \( V \) of a right circular cylinder is given by the formula:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the base,
- \( h \) is the height (or length) 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 of the truck \( h \) is 39 feet.
Now we can plug these values into the volume formula:
\[
V = \pi (4.1)^2 (39)
\]
Calculating \( (4.1)^2 \):
\[
(4.1)^2 = 16.81
\]
Now, substituting this value into the volume formula:
\[
V = \pi (16.81)(39)
\]
Calculating \( 16.81 \times 39 \):
\[
16.81 \times 39 = 656.19
\]
Now, multiplying by \( \pi \) (approximately 3.14159):
\[
V \approx 3.14159 \times 656.19 \approx 2068.58 \text{ cubic feet}
\]
Now that we have the volume of one truck, we can find out how many trucks are needed for 6,175.65 cubic feet of milk:
\[
\text{Number of trucks} = \frac{\text{Total volume of milk}}{\text{Volume of one truck}} = \frac{6175.65}{2068.58} \approx 2.99
\]
Since Raymond cannot order a fraction of a truck, he will need to round up to the nearest whole number. Therefore, he will need **3 trucks**.
Thus, the correct response is:
**Raymond will need 3 trucks since the volume of 1 truck is approximately 2068.58 feet³.**