Cylinder exterior surface area

Hi guys,

ive been given the question; a container made from thin metal is in the shape of a right circular cylinder with a height h cm and a 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 cm2, of the container his given by;

A=(pi)r^2 + 1000/r

Can anybody guide me on how to tackle this problem please? Should I transpose the formula and substitute A for 500cm3 to begin with?

thanks,

Kris :)

Re: Cylinder exterior surface area

Hey Krislton.

What are your formulas for the volume of a cylinder and the area of a cylinder?

Hint: The area of a cylinder (with no top) is the surface area of the cylinder and the bottom (remember circumferences for the cylinder) and the volume of a cylinder and see how to use the information in the volume to simplify the expression for the area.

You have two variables in these: r and h so you will get rid of at least one of them.

Re: Cylinder exterior surface area

Thanks for the input. Too be honest I didn't know the formula for a cylinder surface area but you definitely put me on track.

So to show this I worked out that by transposing (pi)r^2h was the first formula, h=500/(pi)r^2 which meant I could then insert that in the formula which enabled me to show the given formula was correct.

Thanks,

Kris :)

Re: Cylinder exterior surface area

Formula for surface area of a cylinder.

$\displaystyle A=2\pi r h+2\pi r^2$

But you only have one end of the cylinder, so you can get rid of one end of it.

$\displaystyle A=2\pi r h+\pi r^2$

You want to get this right?

$\displaystyle A=\pi r^2 +\frac{1000}{r}$

Formula for volume of a cylinder.

$\displaystyle V=\pi r^2 h$

From there I would solve the volume formula for h, and put it into the area formula. From there, simplify and see what happens. I may be wrong, someone correct me if that turns out to be the case.

Re: Cylinder exterior surface area

Yep you are correct, thanks