If the water completely fills the second container, what is the second container’s diameter?

Question

A cylindrical container with a 3 in. diameter and an 8 in. height is completely filled with water. All of its contents are poured into another cylindrical container that is 2 in. tall.

Answer 1

First the volume of the first cylinder will equal the volume of the second cylinder.

The volume of a cylinder is V = π * r² * h

Volume 1 = Volume 2 . π * r² * h = π * r² * h

Divide both sides by π. You get ---> r² * h = r² * h

We are trying to find the diameter of the second cylinder.

The diameter of the first cylinder is 3 in with a height of 8 in. We need the radius.

D = 2r so the radius of the first cylinder is 1.5 in. The height of the second cylinder is 2 in.

Plug in our values. We get ---> 1.5² * 8 = r² * 2 now simplify

you get ---> 18 = 2 * r² now divide both sides by 2, you get ---> 9 = r²

take the square root of both sides, you get ---> r = 3 in

We need the diameter. D = 2r. D = 2 * 3 in.

Diameter of the second cylinder = 6 in

You are now done

Answer 2

Since all the contents of the first container fit in the second, the volumes must be equal.

Volume1 = Volume2

The formula volume is V=πr²h

Plugging this in we would get

πr₁²h_{1 =} πr₂²h₂ Now we can put in the values and solve it

π(1.5)²(8)₌ π(r₂²)(2) Now simplify The πs will cancel out

18=2r² Divide both sides by 2

18/2=2r²/2 Simplify

9=r² Take the square root of both sides

r=3, Therefore, diameter = 2r = 2(3)

The diameter of the second cylinder is 6 in.