Question

question 4(multiple choice worth 1 points) (06.04 mc) find the total surface area of a cylinder with a height of 7 cm and radius of 3 cm. leave your answer in terms of π. \\(\bigcirc\\) 140π cm² \\(\bigcirc\\) 91π cm² \\(\bigcirc\\) 60π cm² \\(\bigcirc\\) 51π cm²

Explanation:

Step1: Recall the formula for the total surface area of a cylinder

The formula for the total surface area \( S \) of a cylinder is \( S = 2\pi r^2 + 2\pi rh \), where \( r \) is the radius and \( h \) is the height.

Step2: Identify the given values

We are given that \( r = 3 \, \text{cm} \) and \( h = 7 \, \text{cm} \).

Step3: Substitute the values into the formula

First, calculate \( 2\pi r^2 \):
\( 2\pi(3)^2 = 2\pi \times 9 = 18\pi \)
Then, calculate \( 2\pi rh \):
\( 2\pi \times 3 \times 7 = 42\pi \)

Step4: Add the two results together

\( S = 18\pi + 42\pi = 60\pi \)

Answer:

\( 60\pi \, \text{cm}^2 \) (corresponding to the option with \( 60\pi \, \text{cm}^2 \))