Question

select the correct answer.
a company fabricates cast concrete cylindrical columns for a new pavilion. the columns are 3 meters tall and have a radius of 0.6 meters. what is the approximate surface area of a single column?
a. $6.78\\ \text{m}^2$
b. $13.57\\ \text{m}^2$
c. $5.65\\ \text{m}^3$
d. $11.31\\ \text{m}^2$

Explanation:

Step1: Recall total cylinder surface area formula

The total surface area of a cylinder is $SA = 2\pi r^2 + 2\pi r h$, where $r$ is radius, $h$ is height.

Step2: Plug in given values

$r = 0.6\ \text{m}$, $h = 3\ \text{m}$
First calculate $2\pi r^2$:
$2\pi (0.6)^2 = 2\pi(0.36) = 0.72\pi$
Then calculate $2\pi r h$:
$2\pi(0.6)(3) = 3.6\pi$

Step3: Sum the two parts

$SA = 0.72\pi + 3.6\pi = 4.32\pi$

Step4: Compute approximate value

Use $\pi \approx 3.1416$:
$SA \approx 4.32 \times 3.1416 \approx 13.57$

Answer:

B. $13.57\ \text{m}^2$