SOLUTION: You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 170 cm^3, what values of h and r will min

Algebra ->  Circles -> SOLUTION: You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 170 cm^3, what values of h and r will min      Log On


   

Question 990244: You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 170 cm^3, what values of h and r will minimise the total surface area (including the top and bottom faces)? Give your answers correct to 2 decimal places as a list [in brackets] of the form: [ h, r ]
for constants h (height), r (radius), in that order.
THANK YOU
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
v=pi%2Ah%2Ar%5E2, s=2%2Api%2Ar%5E2%2B2pi%2Ar%2Ah, and v=170.


s is for surface area of the can.

v formula gives h=v%2F%28pi%2Ar%5E2%29
s=2pi%2Ar%5E2%2B2pi%2Ar%28v%2F%28pi%2Ar%5E2%29%29
s=2pi%2Ar%5E2%2B2v%2Api%2F%28pi%2Ar%29
highlight%28s=2pi%2Ar%5E2%2B2v%2Fr%29

Find ds/dr and equate to 0, and solve this for r.

ds%2Fdr=4pi%2Ar%2B2v%28-1%29%28r%5E-2%29
ds%2Fdr=4pi-2v%2Fr%5E2=0
highlight_green%28%284pi%2Ar%5E2-2v%29%2Fr%5E2=0%29


Actually, you are looking for highlight%282pi%2Ar%5E2-v=0%29------Solve this for r.