Page 27 - How To Solve Word Problems In Calculus

Substituting into the result of step 2,

50
2
S(x) = 4x + 6x
x 2
300
2
S(x) = 4x +
x
EXAMPLE 9
A cylindrical container with a circular base has a surface area
2
of 64 ft . Express its volume as a function of its radius.
Solution
Step1

r

h

Step2
2
V = πr h

Step3
2
The surface area of the cylinder is 64 ft . We solve for h
in terms of r.

2
2πrh + 2πr = 64
2πrh = 64 − 2πr 2

64 − 2πr 2
h =
2πr
32 − πr 2
h =
πr

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