Page 131 - How To Solve Word Problems In Calculus
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A
10 − h
2r C
B 10
h
D E
6
ABC is similar to
ADE. Therefore, their sides are proportional.
2r 10 − h
=
6 10
20r = 60 − 6h
6h = 60 − 20r
10
h = 10 − r 0 ≤ r ≤ 3
3
By substitution the volume as a function of r is
2
V = πr h
10
V (r ) = πr 2 10 − r
3
10
2 3
= π 10r − r
3
2
V (r ) = π(20r − 10r )
0 = 10πr (2 − r )
r = 0 r = 2
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