SOLUTION: The volume of a right circular cylinder is 294(pi) cm^3. If the height is 1 cm less than its radius, what is its total surface?

Question 1057185: The volume of a right circular cylinder is 294(pi) cm^3. If the height is 1 cm less than its radius, what is its total surface?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The volume(V) of a right circular cylinder is
:
V = pi * r^2 * h, where r is the radius and h is the height
:
We are given that
:
h = r - 1
:
1) pi * r^2 * (r - 1) = 294 * pi
:
r^3 - r^2 - 294 = 0
:
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this cubic has one real solution and two imaginary ones
*************************
:
note the factors are
:
(r - 7) * (r^2 +6r +42) = 0
:
we want r = 7
:
surface area(SA) = (2*pi*r*h) + (2*pi*r^2)
:
*****************************************************************
SA = (2*pi*7*6) + (2*pi*7^2) = 571.7699 cm^2
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:

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