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

Answer:

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

Step-by-step 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 = $2 \times 6 =12$ inches

Volume of cylinder B = $\pi r^{2} h$

                               = $\pi (3)^{2} \times 12$  

                               = $108 \pi inches^3$  

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