Question

find the surface area, to the nearest square centimeter, of a cylinder with radius 4 cm and height 12 cm
a. 48 cm² c. 1206 cm²
b. 402 cm² d. 151 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 surface area \( S \) of a cylinder is given by the formula \( S = 2\pi r^2+ 2\pi rh \), where \( r \) is the radius and \( h \) is the height.

Step2: Substitute the given values

We are given \( r = 4\space\text{cm} \) and \( h = 12\space\text{cm} \). First, calculate \( 2\pi r^2 \):
\( 2\pi r^2=2\times\pi\times4^2 = 2\times\pi\times16=32\pi \)
Then, calculate \( 2\pi rh \):
\( 2\pi rh = 2\times\pi\times4\times12=96\pi \)

Step3: Add the two parts together

\( S=32\pi + 96\pi=128\pi \)

Step4: Approximate the value

Using \( \pi\approx3.14 \), we have \( S\approx128\times3.14 = 401.92\space\text{cm}^2\approx402\space\text{cm}^2 \)

Answer:

b. \( 402\space\text{cm}^2 \)