Page 38 - How To Solve Word Problems In Calculus

8. Let the radius and height of the cylinder be represented by r and h,
respectively.

r

h 10
2

h

2
V = πr h S = 2πrh + 2πr 2
By the Pythagorean theorem,

2
h
2 2
r + = 10
2
h 2
2
r + = 100
4
h 2
2
r = 100 −
4
400 − h 2
2
r =
4
√
400 − h 2
r =
2
It follows by substitution that
√
2 2 2
400 − h 400 − h 400 − h
V = π h S = 2π h + 2π
4 2 4
π 3 π 2
2
V (h) = (400h − h ) S(h) = πh 400 − h + (400 − h )
4 2
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