# Thread: How do i solve ?

1. ## How do i solve ?

I need to calculate the diameter of a cylinder . However the cylinder has a hemisphere as a lid and a flat bottom.
I am given the overall surface area which is 2M square
The overall height is 84cm. Thats it

I can formulate the cylinder diameter if it didn't have a hemisphere top using quadratics however i just cant see how to get this.

SA of hemisphere = 2 pi r square
Sa of base = 1 Pi r square
Cylinder height H= h - r
Cylinder area = 2 pi r H

2. ## Re: How do i solve ?

how much height does the hemisphere add to the cylinder? That should remove one of your variables up there.

3. ## Re: How do i solve ?

it removes the radius from the height and thats my problem i dont know the radius. with out the hemispere its around 3.6 ...
.Total SA ( 2 M sq ) = 3 pi r sq + 2 pi r (.84m)-r ) solve for r ?

can i remove r from + 2 pi r ( .84 - r ) so that its just + 2 pi ( .84) by cancelling ?

yep

5. ## Re: How do i solve ?

So my formula would be SA ( 2m sq ) = 3 pi r Sq + 2 pi (.84 ) ?

6. ## Re: How do i solve ?

no...

it's 2 pi r (0.84) - pi r2 = 2

you cancel the pi r2 terms

incidentally... it's not pi r sq. it's either pi r^2, or pi r2, or even $\pi r^2$

8. ## Re: How do i solve ?

I see a couple problems.

First 2 sq. M is 20,000 sq. cm.

But a more serious problem is that you have $SA = 3\pi r^2 + 2 \pi r (84)$

That's not correct. The entire solid is 84 cm. The cylinder is 84-r cm

so $SA = 3\pi r^2 + 2 \pi r (84-r)$

fix these and resolve it and you should be good to go.

9. ## Re: How do i solve ?

Think this is right now ....cheers for you help and let us know if you agree ?

10. ## Re: How do i solve ?

think this ones right ...?

11. ## Re: How do i solve ?

Originally Posted by civil
think this ones right ...?
I don't really understand why all the trouble with algebra. I'm going to work in meters.

Total height is L, the cylinder height is (L-r)

$SA = \pi r^2 + 2 \pi r^2 + 2 \pi r (L-r)$

$SA = 3 \pi r^2 + 2 \pi r (L-r)$

$SA = 3 \pi r^2 + 2 \pi r L - 2 \pi r^2 = \pi r^2 + 2 \pi r L$

$\pi r^2 + 2 \pi r L - 2 = 0$

$\pi r^2 + 2 \pi r (0.84) - 2 = 0$

$\pi r^2 + (1.68) \pi r - 2 = 0$

$r=0.318542 m$

There is a negative root as well but radii can't be negative.

12. ## Re: How do i solve ?

cant believe ive been so f!£"\$ing blind/stupid/blond cheers for help..... just out of interest why did the quadratic work when wrong ?