SOLUTION: You are the owner of an ice cream shop. You want to design an ice cream cone that holds 60 cubic inches of ice cream inside of the cone (not counting scoops of ice cream on top). W

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Question 1081632: You are the owner of an ice cream shop. You want to design an ice cream cone that holds 60 cubic inches of ice cream inside of the cone (not counting scoops of ice cream on top). What are the dimensions of the cone that will hold exactly 60 cubic inches of ice cream and be the cheapest to make?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You are the owner of an ice cream shop.
You want to design an ice cream cone that holds 60 cubic inches of ice cream inside of the cone (not counting scoops of ice cream on top).
What are the dimensions of the cone that will hold exactly 60 cubic inches of ice cream and be the cheapest to make?
:
Assuming this will be minimum surface area
Using the volume equation
1%2F3pi%2Ar%5E2%2Ah = 60
multiply both sides by 3
pi%2Ar%5E2%2Ah = 180
h = 180%2F%28pi%2Ar%5E2%29
Surface area formula: S.A. = pi%2Ar%2Asqrt%28r%5E2%2Bh%5E2%29
replace h with180%2F%28pi%2Ar%5E2%29
:
S.A. = pi%2Ar%2Asqrt%28r%5E2%2B%28180%2F%28pi%2Ar%5E2%29%29%5E2%29
plot this equation; x=the radius; y=the surface area

:
Minimum surface area occurs when the radius = 3.45"; surface area = 64.2 sq/in
Find the height
h = 180%2F%28pi%2A3.45%5E2%29
h = 4.814 inches high
:
:
Check this by finding the volume using r = 3.45 and h = 4.814
V = 1%2F3pi%2A3.45%5E2%2A4.814
V ~ 60 cu/in
:
:
Summararize; Minimum surface area (cost) when r=3.45; h=4.814