To determine the volume of the tree trunk, we consider the trunk as a cylinder. The formula for the volume [tex]\( V \)[/tex] of a cylinder is given by:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder,
- [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14159.
Given the height of the tree trunk [tex]\( h = 30 \)[/tex] feet and the radius [tex]\( r = 2.5 \)[/tex] feet, we can plug these values into the formula:
[tex]\[ V = \pi (2.5)^2 (30) \][/tex]
First, calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = (2.5)^2 = 6.25 \][/tex]
Next, multiply [tex]\( r^2 \)[/tex] by the height [tex]\( h \)[/tex]:
[tex]\[ 6.25 \times 30 = 187.5 \][/tex]
Finally, multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ V = \pi \times 187.5 \approx 3.14159 \times 187.5 \approx 589.0486225480862 \][/tex]
Therefore, the volume of the tree trunk is approximately [tex]\( 589 \)[/tex] cubic feet.
Comparing this result to the choices given:
[tex]\[ 236 \text{ ft}^3 \][/tex]
[tex]\[ 589 \text{ ft}^3 \][/tex]
[tex]\[ 471 \text{ ft}^3 \][/tex]
[tex]\[ 2,355 \text{ ft}^3 \][/tex]
The value that best represents the volume of the tree trunk is:
[tex]\[ 589 \text{ ft}^3 \][/tex]
So the correct answer is:
[tex]\[ 589 \text{ ft}^3 \][/tex]
