Question

If a paint can hold 2.5 litres of paint in a cylinder work out radius of a the can with a length of 16cm?

Answer 1

Two things, how many cubic centimeters are in a liter and what is the equation for the volume of a cylinder?

Answer 2

1l = 1000cm^3

Answer 3

The equation is Pi * radius^2 * height

Answer 4

So, in the equation for the volume, you know the total volume already, pi is given and the height is the length of the can. You should be able to solve for r from that.

Answer 5

But I dont know how to work backwards from that equation... Could you walk me through it
?

Answer 6

If :
\[V = \pi r^2h\] If we divide both sides by pi and h, we have
\[\frac{V}{\pi h} = r^2\]

Answer 7

7.05

Answer 8

The volume is 2.5..?

Answer 9

ans is 7.5 cm

Answer 10

is this is your ans

Answer 11

Because the height is in centimeters, you need to have the volume also be in centimeters. Because of this, we have to convert Liters to cubic centimeters, as you already related, 1 Liter is 1000 cubic centimeters

Answer 12

What if the length was 20cm?

Answer 13

Then instead of h=16cm, you'd have h=20cm in that equation.

Answer 14

But i dont get how you're supposed to work it out...
Could you walk me through it to the asnwer?

Answer 15

If V is your volume and h is your can length, then:
\[r^2 = \frac{V}{\pi h}, r = \sqrt{\frac{V}{\pi h}}\]
So you just need to plug in your volume in cubic centimeters for V and length in centimeters for h and pi for pi and you should get the radius of the can.

Answer 16

And the anser is..

Answer 17

Whatever:
\[\sqrt{\frac{2.5 L \frac{1000cm^3}{L}}{\pi 16cm}} =\]