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C2 Differentiation - Tearing Hair Out, Please Help!

I honestly have no idea how to approach this question, and it is driving me bonkers! Could someone please tell me what kind of procedure to follow with this, and I bet it's quite simple as well, which just aggravates me even more!

Thank you very much :smile:

A container made from thin metal is in the shape of a rigth circular cylinder with height h cm and base radius r cm. The container has no lid. When full of water, the container holds 500cm3 of water.

Show that the exterior surface area, A cm^2, of the container is given by:

A = 'pi' r ^ 2 + 1000 / r
Reply 1
Toffee_Kid
I honestly have no idea how to approach this question, and it is driving me bonkers! Could someone please tell me what kind of procedure to follow with this, and I bet it's quite simple as well, which just aggravates me even more!

Thank you very much :smile:

A container made from thin metal is in the shape of a rigth circular cylinder with height h cm and base radius r cm. The container has no lid. When full of water, the container holds 500cm3 of water.

Show that the exterior surface area, A cm^2, of the container is given by:

A = 'pi' r ^ 2 + 1000 / r



formula for surface area is pir^2, for the base then 2pi.r times h (the rectangle if you like)

and we know that volume = h x pir^2 = 500

500=hπr2 500 = h\pi r^2

500πr2=h \frac{500}{\pi r^2} = h

sub into area A=πr2+2πrhA = \pi r^2 + 2\pi rh

A=πr2+2πr×500πr2A = \pi r^2 + 2\pi r \times \frac{500}{\pi r^2}

A=πr2+1000rA = \pi r^2 +\frac{1000}{r}

no need for differentiation yet
Reply 2
If you wanted to differentiate it then write out V= and differentiate with respect to x.

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