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

Answer:

$V=18,369\ in^3$

Step-by-step explanation:

step 1

Find the lateral surface of the cylinder (hot water tank)

The lateral area is given by the formula

$LA=2\pi r h$

we have

$r=13\ in\\h=75\ in$

substitute

$LA=2\pi (13)(75)$

$LA=1,950 \pi\ in^2$

step 2

Find the volume of fiberglass composite needed

Multiply the lateral area by the thick

$V=1,950 \pi (3)$

$V=5,850 \pi\ in^3$ -----> exact value

assume

$\pi=3.14$

$V=5,850(3.14)=18,369\ in^3$