Rearanging nightmare.

I can't for the life of me rearrange the following equation. It is part of a differentiation question where I need to create a formula for volume, V. The question is as follows;

A closed cylinder has a total surface area of 600 pi. show that the volume of this cylinder is given by the formula V= 300πr - πr^3

r= radius of cylinder

I know that;
A = 2πrh(2πr^2)
V = πr^2h
therefore
600π = 2πrh(2πr^2) - I need to rearrange this on the left to make h the subject so i can plug it into the volume formula to give me V= 300πr - πr^3.

I've tried a thousand ways but can't seem to get it, please help before I crack! :-?

Reply 1

just george

isnt the surface area:

2 \pi rh + 2 \pi r^2

?

Reply 2

member910132

Original post by monkfishkev

I can't for the life of me rearrange the following equation. It is part of a differentiation question where I need to create a formula for volume, V. The question is as follows;

A closed cylinder has a total surface area of 600 pi. show that the volume of this cylinder is given by the formula V= 300πr - πr^3

r= radius of cylinder

I know that;
A = 2πrh(2πr^2)
V = πr^2h
therefore
600π = 2πrh(2πr^2) - I need to rearrange this on the left to make h the subject so i can plug it into the volume formula to give me V= 300πr - πr^3.

I've tried a thousand ways but can't seem to get it, please help before I crack! :-?

Original post by monkfishkev

I can't for the life of me rearrange the following equation. It is part of a differentiation question where I need to create a formula for volume, V. The question is as follows;

A closed cylinder has a total surface area of 600 pi. show that the volume of this cylinder is given by the formula V= 300πr - πr^3

r= radius of cylinder

I know that;
A = 2πrh(2πr^2)
V = πr^2h
therefore
600π = 2πrh(2πr^2) - I need to rearrange this on the left to make h the subject so i can plug it into the volume formula to give me V= 300πr - πr^3.

I've tried a thousand ways but can't seem to get it, please help before I crack! :-?