diffrentiation and volume?

Question

3) A can is made out of thin sheet metal and is in shape of a right circular cylinder closed at both ends. the radius of the circular cross section of the can is r cm. the height of the can is h cm and the total surface area is A cm^2 . given that the capacity of the can is 31.25*pie cm^3. 
a) show that r^2 *h = 31.25
b)find an expression of A in terms of pie and r only
c) calculate , to one decimal place , the value of dA/dr when r=3
d) show that A has a stationary value when r=2.5 
e) find, giving your answer as a multiple of pie , the stationary value of A establishing whether this is a maximum or minimum value.

Anonymous · Accepted Answer

a) Since the capacity is the volume of the can, we have...

V = πr²h = 31.25π

So r²h = 31.25

b) Then..

A = πr² + 2πrh

But since we want the expression of A in terms of π and r only, we need to take the volume of the can and solve for h, so we can substitute it for the above expression...

r²h = 31.25
h = 31.25/r²

Hence...

A = πr² + 2πr * 31.25/r²
= πr² + 62.5π/r

Good luck!

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diffrentiation and volume?

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