Page 107 - How To Solve Word Problems In Calculus

Step5 (optional)
Since V(0) = 0 and V(10) = 0, the maximum volume
10
must occur when h = √ . The corresponding value of r may
3
h 2
2
be computed from the equation r = 25 −
4
100

2 3
r = 25 −
4
25
= 25 −
3
50
=
3
√ √
50 5 2 5 √
r = √ = √ = 6
3 3 3

50 10 500π
2
The maximum volume is πr h = π √ = √ .
3 3 3 3
EXAMPLE 11
A closed rectangular box with a square base is to have a surface
2
area of 150 in . What is the maximum possible volume such
a box can contain?

Solution
Step1

y
x

x

94