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 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
.
Raymond will need 5 trucks since the volume of 1 truck is 1,004.17 feet cubed .
Raymond will need 1 truck since the volume of 1 truck is 8,234.21 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 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
.
Raymond will need 5 trucks since the volume of 1 truck is 1,004.17 feet cubed .
Raymond will need 1 truck since the volume of 1 truck is 8,234.21 feet3
.
Answers
GPT-4o mini
To determine how many tanker trucks Raymond needs, we first need to calculate the volume of one tanker truck and then see how many are required for the total volume of milk he has.
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 in this case) of the cylinder.
Given:
- The diameter of the truck is 8.2 feet, so the radius \( r \) is half of the diameter:
\[
r = \frac{8.2}{2} = 4.1 \text{ feet}
\]
- The length \( h \) of the truck is 39 feet.
Now, we can calculate the volume:
\[
V = \pi (4.1)^2 (39)
\]
Calculating \( (4.1)^2 \):
\[
(4.1)^2 = 16.81
\]
Now, substituting back into the volume formula:
\[
V = \pi (16.81) (39) \approx 3.14159 \times 16.81 \times 39
\]
Calculating \( 16.81 \times 39 \):
\[
16.81 \times 39 \approx 655.59
\]
Now multiplying by \( \pi \):
\[
V \approx 3.14159 \times 655.59 \approx 2059.79 \text{ cubic feet}
\]
So the volume of one truck is approximately 2059.79 cubic feet.
Now, to determine how many trucks Raymond needs for \( 6,175.65 \, \text{ft}^3 \):
\[
\text{Number of trucks} = \frac{6,175.65}{2059.79} \approx 3
\]
Therefore, Raymond will need **3 trucks** since the volume of 1 truck is approximately **2059.79 ft³**.
Answer:
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 in this case) of the cylinder.
Given:
- The diameter of the truck is 8.2 feet, so the radius \( r \) is half of the diameter:
\[
r = \frac{8.2}{2} = 4.1 \text{ feet}
\]
- The length \( h \) of the truck is 39 feet.
Now, we can calculate the volume:
\[
V = \pi (4.1)^2 (39)
\]
Calculating \( (4.1)^2 \):
\[
(4.1)^2 = 16.81
\]
Now, substituting back into the volume formula:
\[
V = \pi (16.81) (39) \approx 3.14159 \times 16.81 \times 39
\]
Calculating \( 16.81 \times 39 \):
\[
16.81 \times 39 \approx 655.59
\]
Now multiplying by \( \pi \):
\[
V \approx 3.14159 \times 655.59 \approx 2059.79 \text{ cubic feet}
\]
So the volume of one truck is approximately 2059.79 cubic feet.
Now, to determine how many trucks Raymond needs for \( 6,175.65 \, \text{ft}^3 \):
\[
\text{Number of trucks} = \frac{6,175.65}{2059.79} \approx 3
\]
Therefore, Raymond will need **3 trucks** since the volume of 1 truck is approximately **2059.79 ft³**.
Answer:
Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 feet³.