Final answer:
To find the radius of the base of a right circular cylinder, we can use the formula for the total surface area of a cylinder. We substitute the given values into the formula and solve for the radius.
Step-by-step explanation:
To find the radius of the base of a right circular cylinder, we need to use the formula for the total surface area of a cylinder, which is given by:
A = 2πrh + 2πr²
In this case, we are given that the total surface area is 84π square centimeters and the altitude (height) is 11 centimeters. We can substitute these values into the formula and solve for the radius, r:
84π = 2πr(11) + 2πr²
After simplifying the equation, we can solve for r using either factoring, completing the square, or the quadratic formula. The solution will give us the radius of the base of the cylinder.