Set up an equation and solve the problem. The total surface area of a right circular cylinder is 36 $\pi$ square centimeters. If a radius of the base and the altitude of the cylinder are the same length, find the length of a radius.
A) 4 centimeters
B) 9 centimeters
C) 3 centimeters
D) 2 centimeters
E) none of these

Question

Quizplus · Accepted Answer

Let r be the radius and h be the altitude of the cylinder.
The formula for the total surface area of a right circular cylinder is: A = 2$\pi$r(r + h)
Since the radius and the altitude are the same length, we have: A = 2$\pi$r(2r) = 4$\pi$r^2
We are given that the total surface area is 36$\pi$, so we can set up an equation:
4$\pi$r^2 = 36$\pi$
Divide both sides by 4$\pi$:
r^2 = 9
Take the square root of both sides:
r = 3 or r = -3
Since radius has to be a positive length, the only valid solution is r = 3. Therefore, the length of the radius is 3 centimeters.

Set Up an Equation and Solve the Problem π\piπ Square Centimeters

Set Up an Equation and Solve the Problem $\pi$ Square Centimeters