If the volume of the cone is 480 in?, what is its surface area? Use 3.14 for it and round the answer to the nearest hundredth.
HELP ASAP

This is a two part problem. The first part involves using the given volume and height to determine the radius r.

V = volume of the cone

V = (1/3)pi*r^2*h

480 = (1/3)*3.14*r^2*8

480*3 = 3.14*8*r^2

1440 = 25.12r^2

25.12r^2 = 1440

r^2 = 1440/(25.12)

r^2 = 57.32484076 approximately

r = sqrt(57.32484076)

r = 7.57131697659

r = 7.5713

That's the approximate radius value.

The second part is where we compute the surface area based on the radius we found, and also the given height.

SA = surface area of the cone

SA = pi*r^2 + pi*r*sqrt(r^2 + h^2)

SA = 3.14*(7.5713)^2 + 3.14*7.5713*sqrt((7.5713)^2 + 8^2)

SA = 441.862415073011

SA = 441.86

The units for the surface area are in square inches, which abbreviates to in^2.

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