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March 5, 2015

March 5, 2015

Posted by **Mat** on Monday, May 20, 2013 at 10:17pm.

The containers need to hold 25litres and must be cylindrical in shape. What

dimensions will ensure that the least amount of plastic is used to create the

containers. (Note: the volume and surface area of cylinders are V =πr2h and

S = 2πr2 + 2πrh respectively)

- calculus -
**Steve**, Tuesday, May 21, 2013 at 11:36amv=pi r^2 h = 25, so

h = 25/(pi r^2)

a = 2πr^2 + 2πrh

= 2πr^2 + 2πr*25/(πr^2)

= 2πr^2 + 50/r

da/dr = 4πr - 50/r^2

= (4πr^3 - 50)/r^2

since r≠0, da/dr=0 when 4πr^3 = 50

r = ∛(25 / 2π)

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