Question

A graduated cylinder that is 24cm tall can hold 1L of water. What is the radius of the cylinder? What is the height of the 500 ml mark? The 250 ml mark? Recall that 1 liter is equal to 1000 millimeters

Answer 1

Part A) The radius of the cylinder is
`r=\sqrt{(125)/(3\pi)}\ cm`

Part B) The height of the 500 ml mark is
`12\ cm`

Part C) The height of the 250 ml mark is
`6\ cm`

Explanation:

Part A) What is the radius of the cylinder?

we know that

The volume of a cylinder is equal to

`V=\pi r^(2) h`

we have

`V=1\ l=1,000\ ml=1,000\ cm^(3)`

`h=24\ cm`

substitute and solve for r

`1,000=\pi r^(2) (24)`

`r^(2)=(1,000)/(24\pi)`

`r=\sqrt{(1,000)/(24\pi)}\ cm`

simplify

`r=\sqrt{(125)/(3\pi)}\ cm`

Part B) What is the height of the 500 ml mark?

using proportion

`(24)/(1,000)(cm)/(ml)=(x)/(500)(cm)/(ml)\\ \\x=500*24/1,000\\\\x=12\ cm`

Part C) What is the height of the 250 ml mark?

using proportion

`(24)/(1,000)(cm)/(ml)=(x)/(250)(cm)/(ml)\\ \\x=250*24/1,000\\\\x=6\ cm`