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Raymond owns a dairy farm and has to order tanker trucks, which are in the shape of right circular cylinders, to pick up his mi...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)
of milk?(1 point)
Answers
GPT-4o mini
To determine how many tanker trucks Raymond will need, we first need to calculate the volume of one tanker truck in the shape of a right circular cylinder.
The volume \( V \) of a cylinder is calculated using the formula:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (length) of the cylinder.
1. **Calculate the radius:**
The diameter of the truck is 8.2 feet, so the radius \( r \) is half of the diameter:
\[
r = \frac{8.2}{2} = 4.1 \text{ feet}
\]
2. **Use the length of the truck as the height:**
The length of the truck \( h \) is 39 feet.
3. **Substitute \( r \) and \( h \) into the volume formula:**
\[
V = \pi (4.1)^2 (39)
\]
First, calculate \( r^2 \):
\[
(4.1)^2 = 16.81
\]
Now substitute:
\[
V = \pi (16.81)(39)
\]
Calculate \( 16.81 \times 39 \):
\[
16.81 \times 39 = 655.59
\]
Now multiply by \( \pi \) (approximately 3.14159):
\[
V \approx 3.14159 \times 655.59 \approx 2057.43 \text{ cubic feet}
\]
4. **Determine how many trucks are needed:**
Now we need to find out how many tanker trucks are required for the total volume of milk, which is 6,175.65 cubic feet:
\[
\text{Number of trucks} = \frac{\text{Total volume of milk}}{\text{Volume of one truck}} = \frac{6175.65}{2057.43}
\]
Performing the division:
\[
\text{Number of trucks} \approx 3.00
\]
Since we cannot have a fraction of a truck, we need to round up to the nearest whole number. Thus, Raymond will need **4 tanker trucks** to transport his milk.
The volume \( V \) of a cylinder is calculated using the formula:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (length) of the cylinder.
1. **Calculate the radius:**
The diameter of the truck is 8.2 feet, so the radius \( r \) is half of the diameter:
\[
r = \frac{8.2}{2} = 4.1 \text{ feet}
\]
2. **Use the length of the truck as the height:**
The length of the truck \( h \) is 39 feet.
3. **Substitute \( r \) and \( h \) into the volume formula:**
\[
V = \pi (4.1)^2 (39)
\]
First, calculate \( r^2 \):
\[
(4.1)^2 = 16.81
\]
Now substitute:
\[
V = \pi (16.81)(39)
\]
Calculate \( 16.81 \times 39 \):
\[
16.81 \times 39 = 655.59
\]
Now multiply by \( \pi \) (approximately 3.14159):
\[
V \approx 3.14159 \times 655.59 \approx 2057.43 \text{ cubic feet}
\]
4. **Determine how many trucks are needed:**
Now we need to find out how many tanker trucks are required for the total volume of milk, which is 6,175.65 cubic feet:
\[
\text{Number of trucks} = \frac{\text{Total volume of milk}}{\text{Volume of one truck}} = \frac{6175.65}{2057.43}
\]
Performing the division:
\[
\text{Number of trucks} \approx 3.00
\]
Since we cannot have a fraction of a truck, we need to round up to the nearest whole number. Thus, Raymond will need **4 tanker trucks** to transport his milk.