Question

quiz 2. surface areas of circular solids
what is the surface area of a right cylinder which has a base with radius 9 units and has a height of 12 units?
508.7 units²
678.2 units²
1,186.9 units²
1,256.0 units²

Explanation:

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

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

Step2: Substitute the given values

Given \( r = 9 \) units and \( h = 12 \) units. First, calculate \( 2\pi r^2 \): \( 2\pi(9)^2 = 2\pi\times81 = 162\pi \). Then, calculate \( 2\pi rh \): \( 2\pi\times9\times12 = 216\pi \).

Step3: Sum the two parts

Add the two results: \( SA = 162\pi + 216\pi = 378\pi \). Now, approximate \( \pi \approx 3.1416 \), so \( 378\times3.1416 \approx 378\times3.14 = 1186.92 \approx 1186.9 \) units².

Answer:

1,186.9 units²