SOLUTION: An open-topped conical birthday hat is to have volume 55 cm3. Determine the minimum possible amount of material used in making this pot? Show your complete solution and diagram

Algebra ->  Bodies-in-space -> SOLUTION: An open-topped conical birthday hat is to have volume 55 cm3. Determine the minimum possible amount of material used in making this pot? Show your complete solution and diagram      Log On


   

Question 1189147: An open-topped conical birthday hat is to have volume 55 cm3. Determine the minimum possible amount of material used in making this pot? Show your complete solution and diagram
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An open-topped conical birthday hat is to have volume 55 cm3.
Determine the minimum possible amount of material used in making this pot?
:
The vol of a cone
V = 1%2F3pi%2Ar%5E2%2Ah
1%2F3pi%2Ar%5E2%2Ah = 55
Get rid of the fraction mult by 3
pi%2Ar%5E2%2Ah = 165
h = 165%2F%28pi%2Ar%5E2%29
:
Find the area of the cone material
A = pi%2Ar%2Asqrt%28r%5E2%2Bh%5E2%29
replace h with 165%2F%28pi%2Ar%5E2%29
A = pi%2Ar%2Asqrt%28r%5E2%2B%28165%2F%28pi%2Ar%5E2%29%29%5E2%29
Graphically, radius on the horizontal, area on the vertical

Minimum material used when r = 1.4 cm, it then uses 11 sq/cm of material
"
"
you can check this, find the height (h) using r=1.4, then calculate volume