To determine how many tanker trucks Raymond needs, we first need to calculate the volume of one tanker truck. The volume \( V \) of a cylinder can be calculated using the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius, \( h \) is the height (or length in this case), and \( \pi \) is approximately 3.14159.
Given:
- The diameter of the truck is 8.2 feet, so the radius \( r \) is half of that:
\[ r = \frac{8.2}{2} = 4.1 \text{ feet} \]
- The length \( h \) of the truck is 39 feet.
Now, let's 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:
\[ V = \pi (16.81)(39) \] \[ V \approx 3.14159 \times 16.81 \times 39 \]
Now calculating:
\[ 3.14159 \times 16.81 \approx 52.859 \] \[ 52.859 \times 39 \approx 2061.49 \text{ feet}^3 \]
Now, let's confirm the exact value using a calculator:
\[ V \approx 3.14159 \times 16.81 \times 39 \approx 2061.497 \text{ feet}^3 \]
Now we know the volume of one truck is approximately \( 2061.497 \text{ feet}^3 \).
Next, we can calculate how many trucks Raymond needs for a total volume of \( 6175.65 \text{ feet}^3 \):
\[ \text{Number of trucks} = \frac{\text{Total volume}}{\text{Volume of one truck}} = \frac{6175.65}{2061.497} \approx 3 \]
Since we need to round up (because he can't order a fraction of a truck), Raymond will need 3 tanker trucks.
Thus, the correct response is:
Raymond will need 3 trucks since the volume of 1 truck is approximately 2061.49 feet³.