SOLUTION: If a cone has a volume of 500cm^3. What is it's radius and hight with the smallest surface area

Question 935948: If a cone has a volume of 500cm^3. What is it's radius and hight with the smallest surface area

Found 2 solutions by Alan3354, ankor@dixie-net.com:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Including the base? or just the lateral area?
PS it's = it is
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If a cone has a volume of 500cm^3.
What is it's radius and height with the smallest surface area.
:
Find the relationship between the height and radius using the volume

multiply both sides by 3

divide both sides by

:
Surface area formula:
S.A =
replace h with
S.A. =
Graph this equation

minimum surface area occurs when r = 7 cm, about 264 sq cm
Find the height
h =
h = 9.7 cm
:
See if that checks out by finding the vol with these value
v = *
v = 498 cu/cm, is that close enough?
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