Question

as part of a survey, jessie measures the height of a tree trunk as 12 feet and the diameter as 2 feet. she models the trunk of the tree with a geometric shape to calculate its lateral surface area in order to estimate how much bark covers the tree. which one of these statements is true? a) the tree trunk can be modeled by a cone, and its lateral surface area is approximately 37.8 square feet. b) the tree trunk can be modeled by a cone, and its lateral surface area is approximately 41.0 square feet. c) the tree trunk can be modeled by a cylinder, and its lateral surface area is approximately 75.4 square feet. d) the tree trunk can be modeled by a cylinder, and its lateral surface area is approximately 81.6 square feet.

Explanation:

Step1: Identify the geometric - shape

A tree trunk is more like a cylinder. The formula for the lateral - surface area of a cylinder is $A = 2\pi rh$, where $r$ is the radius and $h$ is the height.

Step2: Calculate the radius

Given the diameter $d = 2$ feet, the radius $r=\frac{d}{2}=\frac{2}{2}=1$ foot, and the height $h = 12$ feet.

Step3: Calculate the lateral - surface area

Substitute $r = 1$ and $h = 12$ into the formula $A = 2\pi rh$. So $A=2\pi\times1\times12 = 24\pi\approx24\times3.14 = 75.36\approx75.4$ square feet.

Answer:

C. The tree trunk can be modeled by a cylinder, and its lateral surface area is approximately 75.4 square feet.