Question

find the surface area, to the nearest square centimeter, of a cylinder with diameter 6 cm and height 8 cm.
a. 48 cm² \tc. 207 cm²
b. 452 cm² \td. 72 cm²

please select the best answer from the choices provided

○ a
○ b
○ c
○ d

Explanation:

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

The formula for the 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: Find the radius

Given the diameter \( d = 6 \) cm, the radius \( r=\frac{d}{2}=\frac{6}{2} = 3 \) cm. The height \( h = 8 \) cm.

Step3: Substitute the values into the formula

First, calculate \( 2\pi r^2 \):
\( 2\pi(3)^2=2\pi\times9 = 18\pi \)
Then, calculate \( 2\pi rh \):
\( 2\pi\times3\times8=48\pi \)
Now, add these two parts together:
\( S=18\pi + 48\pi=66\pi \)

Step4: Calculate the numerical value

Using \( \pi\approx3.14 \), we have \( S\approx66\times3.14 = 207.24 \approx 207 \) \( \text{cm}^2 \)

Answer:

C. \( 207 \text{ cm}^2 \)