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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

Respuesta :

calculista

Answer:

[tex]V=18,369\ in^3[/tex]

Step-by-step explanation:

step 1

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

The lateral area is given by the formula

[tex]LA=2\pi r h[/tex]

we have

[tex]r=13\ in\\h=75\ in[/tex]

substitute

[tex]LA=2\pi (13)(75)[/tex]

[tex]LA=1,950 \pi\ in^2[/tex]

step 2

Find the volume of fiberglass composite needed

Multiply the lateral area by the thick

[tex]V=1,950 \pi (3)[/tex]

[tex]V=5,850 \pi\ in^3[/tex] -----> exact value

assume

[tex]\pi=3.14[/tex]

[tex]V=5,850(3.14)=18,369\ in^3[/tex]

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