SOLUTION: The surface area of a cylinder is 600 pi centimeters squared. If the radius is 1 cm, find the volume in terms of pi.

Question 1082549: The surface area of a cylinder is 600 pi centimeters squared. If the radius is 1 cm, find the volume in terms of pi.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula for surface area of a cylinder is:

s = 2*pi*r^2 + 2*pi*r*h

since you know the surface area is equal to 600 square meters and the radius is equal to 1, this formula becomes:

600 = 2*pi*1^2 + 2*pi*1*h

since 1^2 = 1 and anything times 1 is anything, this formula becomes:

600 = 2*pi + 2*pi*h

factor out the 2*pi and the formula becomes:

600 = 2*pi*(1+h)

divide both sides of this equation by 2*pi and you get:

600/(2*pi) = 1+h

the parentheses are necessary since you are dividing by (2*pi).
without them, you would have 600/2*pi which would divide 600 by 2 and then multiply the result by pi - a totally different result.

subtract 1 from both sides of this equation to get:

600/(2*pi)-1 = h

solve for h to get h = 94.49296586

the formula for the volume of a cylinder is v = pi*r^2*h

since r = 1, then r^2 = 1 and the formula becomes v = pi*h

since h = 94.49296586, then the formula becomes v = 94.49296586*pi

solve for v to get v = 296.8584073 cubic meters.

while this is correct, it might not be what you were asked to do.

i believe you were asked to find the volume in terms of pi.

in that case, you would do the following:

s = 2*pi*r^2 + 2*pi*r*h

since r = 1, this becomes:

s = 2*pi + 2*pi*h

factor out the 2*pi and you get s = 2*pi*(1+h)

since s = 600 square meters, you get 600 = 2*pi*(1+h)

solve for h to get h = 600/(2*pi)-1.

volume formula is v = pi*r^2*h

since h = 600/(2*pi)-1, the formula becomes v = pi*r^2*(600/(2*pi)-1).

simplify to get v = pi*r^2*600/(2*pi) - pi*r^2*1

simplify further to get v = r^2*600/2 - pi*r^2

simplify further to get v = 300*r^2 - pi*r^2

since r = 1, this simplifies further to v = 300 - pi

that's your volume in terms of pi.

evaluate this to get v = = 296.8584073 cubic meters.

that's what we got before when we have determined the value of h.

this time, however, the volume is in terms of pi as requested by the problem statement.

your solution is that v = 300 - pi.

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