Question

Calculate the height of a right circular cylinder with a surface area of 300 square inches and a radius of 5 inches to the nearest hundredth.

Short answer

Answer: The height of the right circular cylinder is approximately 4.54 inches.

Step-by-step solution

Write down the formula for the surface area of a right circular cylinder

The formula for the surface area (A) of a right circular cylinder is: A = 2πr^2 + 2πrh Where r is the radius of the base, h is the height of the cylinder, and π (pi) is a constant, approximately 3.1415.

Substitute the given values

We are given the surface area A = 300 square inches and the radius r = 5 inches. Plug in these values into the surface area formula: 300 = 2π(5)^2 + 2π(5)h

Simplify the equation

First, calculate the value of 2π(5)^2: 2π(5)^2 = 50π Now, the equation becomes: 300 = 50π + 10πh

Isolate the term with the height (h)

To solve for h, subtract 50π from both sides of the equation: 300 - 50π = 10πh

Solve for the height (h) of the cylinder

Now, divide both sides of the equation by 10π to find the height: h = (300 - 50π) / 10π h ≈ (300 - 157.08) / 31.415 ≈ 4.54

Round the answer to the nearest hundredth

The height of the right circular cylinder is approximately 4.54 inches.