Question

A thermal insulated sleeve is used to cover the lateral surface of a hot water heater to help improve efficiency. The hot water tank is a cylinder with a 13 inch radius and a 75 inch height. The sleeve is 3 inches thick. The insulating material that makes up the sleeve is a fiberglass composite. How many cubic inches of fiberglass composite are needed to create each sleeve?

v= in3

Answer 1

To find the volume of fiberglass composite needed for the sleeve, calculate the volume of the larger cylinder with a 16-inch radius, calculate the volume of the smaller cylinder with a 13-inch radius, and subtract the smaller from the larger.

Step-by-step explanation:

To calculate the volume of the fiberglass composite needed to create the insulating sleeve for the hot water heater, we need to determine the volume of the larger cylinder (the sleeve plus the heater) and subtract the volume of the smaller cylinder (the heater). The larger cylinder has a radius of 13 inches (the heater) plus 3 inches (the thickness of the sleeve), making it 16 inches in total. The height remains 75 inches. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

Step 1: Calculate the volume of the larger cylinder using the radius of the larger cylinder (16 inches):
Vlarge = π(16 inches)²(75 inches).

Step 2: Calculate the volume of the smaller cylinder using the radius of the heater (13 inches):
Vsmall = π(13 inches)²(75 inches).

Step 3: Subtract the volume of the smaller cylinder from the volume of the larger cylinder to get the volume of the fiberglass composite:
Vcomposite = Vlarge - Vsmall.

Perform these calculations to determine the required cubic inches of fiberglass composite.