Question

lesson 8: surface area and volume
cylinder surface area and volume formulas
what is the surface area of a cylinder with a radius of 2 inches and a height of 12 inches? use 3.14 for π and round to the nearest whole number.
a. 327 inches squared
b. 151 inches squared
c. 201 inches squared
d. 176 inches squared
check answer

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: Substitute the given values

Given \( r = 2 \) inches, \( h = 12 \) inches, and \( \pi = 3.14 \).
First, calculate the area of the two circular bases: \( 2\pi r^2 = 2\times3.14\times2^2 \)
\( 2\times3.14\times4 = 25.12 \)
Then, calculate the lateral (curved) surface area: \( 2\pi rh = 2\times3.14\times2\times12 \)
\( 2\times3.14\times24 = 150.72 \)

Step3: Sum the two areas

Add the area of the bases and the lateral surface area: \( S = 25.12 + 150.72 = 175.84 \)

Step4: Round to the nearest whole number

\( 175.84 \) rounded to the nearest whole number is \( 176 \).

Answer:

d. 176 inches squared