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C1 Question

The question is from the A1 practice paper, it says:
A container made from thin metal is in the shape of a right circular cylinder with height h cm and base radius r cm. The container has no lid. When full of water, the container holds 500 cm3cm^3 of Water.

Show that the exterior surface area, A cm2cm^2 of the container is given by

A = π\pir2r^2 + 1000r\frac{1000}{r}

What I have done is volume = π\pir2r^2 ×h=500\times h = 500 cm3cm^3

exterior surface area = 2 π\pirhrh  +\ + π\pir2r^2

I don't know where to go from here, the mark scheme says it's 2π\pirhrh  +\ + π\pir2r^2
But why 2? wouldn't that give the area of the 'slant' twice?
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Avatar for davros
davros
16
Original post by NotNotBatman
The question is from the A1 practice paper, it says:
A container made from thin metal is in the shape of a right circular cylinder with height h cm and base radius r cm. The container has no lid. When full of water, the container holds 500 cm3cm^3 of Water.

Show that the exterior surface area, A cm2cm^2 of the container is given by

A = π\pir2r^2 + 1000r\frac{1000}{r}

What I have done is volume = π\pir2r^2 ×h=500\times h = 500 cm3cm^3

exterior surface area = 2 π\pirhrh  +\ + π\pir2r^2

I don't know where to go from here, the mark scheme says it's 2π\pirhrh  +\ + π\pir2r^2
But why 2? wouldn't that give the area of the 'slant' twice?


What 'slant'? You do know that the curved surface area of a cylinder is 2πrh2\pi r h don't you?

You just need to rearrange your volume equation to give h in terms of r, then substitute into the equation for total surface area, then the result drops out :smile:
Original post by davros
What 'slant'? You do know that the curved surface area of a cylinder is 2πrh2\pi r h don't you?

You just need to rearrange your volume equation to give h in terms of r, then substitute into the equation for total surface area, then the result drops out :smile:


I get it, I was using the formula for area of curved surface of a cone. I've never used the formula for the curved surface area of a cylinder but it makes sense that it's circumference X height. Thank you!
Reply 3
Avatar for davros
davros
16
Original post by NotNotBatman
I get it, I was using the formula for area of curved surface of a cone. I've never used the formula for the curved surface area of a cylinder but it makes sense that it's circumference X height. Thank you!


Haha - I did wonder if you were thinking of a cone when you mentioned 'slant'. A cylinder is MUCH easier because you can just 'unwrap' it and flatten it out to get the curved surface area!

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