Question

Karen calculates the volume of cylinder A with a radius of 3 inches, and a height of 6 inches. The volume of this cylinder is 54π in3. Cylinder B also has a radius of 3 inches, but the height is doubled. What is the relationship between the volumes of the two cylinders?

Answer 1

the volume of B is twice that of A
if Vb=2hpir^2
and Va=hpir^2

compare
2hpir^2
hpir^2

twic as big

Volume of B is 2 times that of Volume of A

Answer 2

`2(\text{Volume of cylinder A})= \text{Volume of cylinder B }`

Explanation:

Cylinder A:

Radius = 3 inches

Height = 6 inches

Volume =
`54\pi inches^3`

Cylinder B:

We are given that Cylinder B also has a radius of 3 inches, but the height is doubled.

Radius = 3 inches

Height =
`2 * 6 =12` inches

Volume of cylinder B =
`\pi r^(2)  h`

=
`\pi (3)^(2) * 12`

=
`108 \pi inches^3`

Thus the volume of cylinder B is 108π cubic inches

Volume of Cylinder A = 54 π cubic inches

Since
`2(54\pi )=108\pi`

So, twice the volume of cylinder A = Volume of cylinder B

`2(\text{Volume of cylinder A})= \text{Volume of cylinder B }`

Hence the relationship between the volumes of the two cylinders is
`2(\text{Volume of cylinder A})= \text{Volume of cylinder B }`