SOLUTION: Find the dimensions of the cone of maximum volume if the diameter and height of the cone total 24 cm.

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Question 1013915: Find the dimensions of the cone of maximum volume if the diameter and height of the cone total 24 cm.
Answer by josgarithmetic(39633) About Me  (Show Source):
You can put this solution on YOUR website!
Height h
Diameter d
v for volume

system%28v=%281%2F4%29h%2Api%2Ad%5E2%2Ch%2Bd=24%29

v=%281%2F4%29pi%2A%2824-d%29%2Ad%5E2
v=%281%2F4%29pi%2824d%5E2-d%5E3%29
v=6pi%2Ad%5E2-%28pi%2F4%29d%5E3

A calculus practice, derivative:
dv%2Fdd=12pi%2Ad-%283pi%2F4%29d%5E2

12pi%2Ad-%283pi%2F4%29d%5E2=0
d%2812pi-%283pi%2F4%29d%29=0
d=0%2CNotReasonable
-
12pi=%283pi%2F4%29d
d=12%2A4%2Api%2F%283pi%29
d=4%2A4
highlight%28d=16%29
and the corresponding height, highlight%28h=8%29.

Those should give the maximum volume using that restriction for h and d.