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 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
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 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
Answers
GPT-4o mini
To determine how many tanker trucks Raymond needs, we first need to calculate the volume of one tanker truck, which is 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 of the base of the cylinder,
- \( h \) is the height (or length) of the cylinder.
### Given Data:
- Length of the truck (height \( h \)) = 39 feet
- Diameter of the truck = 8.2 feet
- Therefore, the radius \( r \) = diameter / 2 = 8.2 / 2 = 4.1 feet
### Volume Calculation:
\[
V = \pi (4.1)^2 (39)
\]
First, calculate \( (4.1)^2 \):
\[
(4.1)^2 = 16.81
\]
Now multiply by height:
\[
16.81 \times 39 = 654.39
\]
Now, multiply by \( \pi \):
\[
V \approx 3.14159 \times 654.39 \approx 2056.47 \text{ feet}^3
\]
### Number of Trucks Required:
Raymond has a total volume of milk of \( 6,175.65 \text{ feet}^3 \). To find out how many trucks are needed, we divide the total volume of milk by the volume of one truck:
\[
\text{Number of trucks} = \frac{6175.65}{2056.47} \approx 3
\]
Therefore, Raymond will need **3 trucks**.
From the options given, the correct one is:
**Raymond will need 3 trucks since the volume of 1 truck is approximately 2,055.47 feet^3.** (This should be labeled as 2,056.47 feet cubed.)
The formula for the volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height (or length) of the cylinder.
### Given Data:
- Length of the truck (height \( h \)) = 39 feet
- Diameter of the truck = 8.2 feet
- Therefore, the radius \( r \) = diameter / 2 = 8.2 / 2 = 4.1 feet
### Volume Calculation:
\[
V = \pi (4.1)^2 (39)
\]
First, calculate \( (4.1)^2 \):
\[
(4.1)^2 = 16.81
\]
Now multiply by height:
\[
16.81 \times 39 = 654.39
\]
Now, multiply by \( \pi \):
\[
V \approx 3.14159 \times 654.39 \approx 2056.47 \text{ feet}^3
\]
### Number of Trucks Required:
Raymond has a total volume of milk of \( 6,175.65 \text{ feet}^3 \). To find out how many trucks are needed, we divide the total volume of milk by the volume of one truck:
\[
\text{Number of trucks} = \frac{6175.65}{2056.47} \approx 3
\]
Therefore, Raymond will need **3 trucks**.
From the options given, the correct one is:
**Raymond will need 3 trucks since the volume of 1 truck is approximately 2,055.47 feet^3.** (This should be labeled as 2,056.47 feet cubed.)