Question

1. what prism or other 3 - dimensional shape would you use to model the tree trunk below? (rectangular prism, triangular prism, square prism, or cylinder). if the height of the tree trunk is 13 ft and the radius is 1.5 ft, what is the volume in cubic feet? round to the nearest tenth. enter your answer and also show your work to demonstrate how you determined your answer.

Explanation:

Step1: Identify the 3 - D shape

A tree trunk is best modeled as a cylinder.

Step2: Recall the volume formula for a cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step3: Substitute the given values

We are given $r = 1.5$ ft and $h=13$ ft. Substitute into the formula: $V=\pi\times(1.5)^{2}\times13$.
First, calculate $(1.5)^{2}=2.25$. Then $V=\pi\times2.25\times13$.
$V = 29.25\pi$.

Step4: Calculate the numerical value

Using $\pi\approx3.14$, we have $V\approx29.25\times3.14 = 91.845$.

Step5: Round to the nearest tenth

Rounding $91.845$ to the nearest tenth gives $V\approx91.8$ cubic feet.

Answer:

The 3 - dimensional shape to model the tree trunk is a cylinder and its volume is approximately $91.8$ cubic feet.