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

Question 993779: 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 rothauserc(4718) (Show Source): You can put this solution on YOUR website!
A right circular cylinder with a given volume has the property that h = 2r where h is the height and r is the radius - this cylinder also has minimal surface area
********************************************************************************
Volume(V) of a right circular cylinder = pi*r^2*h
********************************************************************************
170 = pi*r^2(2*r)
170 = pi*2*r^3
r^3 = 170 / (2*pi) = 27.056340322
r = (27.056340322)^(1/3) = 3.002085229 approx 3.00
h = 2 * 3.002085229 = 6.004170458 approx 6.00
[ h, r ] = [ 6.00, 3.00 ]

RELATED QUESTIONS
You have been asked to design a can shaped like a right circular cylinder with height h... (answered by josgarithmetic)

You have been asked to design a can shaped like a right circular cylinder with height h... (answered by Theo,Fombitz)

You have been asked to design a can shaped like a right circular cylinder with height h... (answered by KMST)

A right circular cylinder of radius r and height h has volume given by V=πr^2h and... (answered by ankor@dixie-net.com)

please help me solve this equation: suppose you have a right circular cylinder with... (answered by Alan3354)

A right-circular cylinder has a radius r cm and a height h cm. Given that h + r = 30,... (answered by richard1234)

A right circular cylinder has a volume of 130 cubic inches. Find the radius and height... (answered by ikleyn)

Can someone please tell me how I calculate the radius of a cylinder when only height is... (answered by stanbon)

What is the length of the diagonal of the largest cube that can be cut from a right... (answered by Fombitz)