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
6
,
175.65
feet
3
of milk?(1 point)
Responses
Raymond will need 8 trucks since the volume of 1 truck is 502.09 feet3
502.09
feet
3
.
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
2
,
058.55
feet
3
.
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
1
,
004.17
feet
3
.
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
8
,
234.21
feet
3
.
6
,
175.65
feet
3
of milk?(1 point)
Responses
Raymond will need 8 trucks since the volume of 1 truck is 502.09 feet3
502.09
feet
3
.
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
2
,
058.55
feet
3
.
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
1
,
004.17
feet
3
.
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
8
,
234.21
feet
3
.
Answers
GPT-4o mini
To determine 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 given by:
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height (or length in this case) of the cylinder.
1. **Calculate the radius:**
The diameter of the truck is given as 8.2 feet. Therefore, the radius \( r \) is:
\[
r = \frac{d}{2} = \frac{8.2 \text{ feet}}{2} = 4.1 \text{ feet}
\]
2. **Calculate the volume of one truck:**
The length \( h \) of the truck is 39 feet. Now plug in the values into the volume formula:
\[
V = \pi (4.1 \text{ feet})^2 (39 \text{ feet})
\]
\[
V = \pi (16.81 \text{ feet}^2) (39 \text{ feet})
\]
\[
V = \pi (655.59 \text{ feet}^3)
\]
\[
V \approx 3.14159 \times 655.59 \text{ feet}^3 \approx 2058.55 \text{ feet}^3
\]
3. **Determine how many trucks are needed:**
Now, divide the total volume of milk by the volume of one truck:
\[
\text{Number of trucks} = \frac{6175.65 \text{ feet}^3}{2058.55 \text{ feet}^3} \approx 3
\]
Since Raymond cannot order a fraction of a truck, he would need to round up to the nearest whole truck. Hence, he will need **3 trucks**.
Therefore, the correct response is:
**Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 feet³.**
\[
V = \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height (or length in this case) of the cylinder.
1. **Calculate the radius:**
The diameter of the truck is given as 8.2 feet. Therefore, the radius \( r \) is:
\[
r = \frac{d}{2} = \frac{8.2 \text{ feet}}{2} = 4.1 \text{ feet}
\]
2. **Calculate the volume of one truck:**
The length \( h \) of the truck is 39 feet. Now plug in the values into the volume formula:
\[
V = \pi (4.1 \text{ feet})^2 (39 \text{ feet})
\]
\[
V = \pi (16.81 \text{ feet}^2) (39 \text{ feet})
\]
\[
V = \pi (655.59 \text{ feet}^3)
\]
\[
V \approx 3.14159 \times 655.59 \text{ feet}^3 \approx 2058.55 \text{ feet}^3
\]
3. **Determine how many trucks are needed:**
Now, divide the total volume of milk by the volume of one truck:
\[
\text{Number of trucks} = \frac{6175.65 \text{ feet}^3}{2058.55 \text{ feet}^3} \approx 3
\]
Since Raymond cannot order a fraction of a truck, he would need to round up to the nearest whole truck. Hence, he will need **3 trucks**.
Therefore, the correct response is:
**Raymond will need 3 trucks since the volume of 1 truck is 2,058.55 feet³.**