Question

There are two right circular cylinders that have the same height, 45 centimeters. The radius of the smaller cylinder is 22 centimeters and the radius of the larger cylinder is 6 times greater than that of the smaller cylinder. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder?

a. 6:1
b. 12:1
c. 36:1
d. 150:1

Will someone please explain to me how to do this? Thanks in advanced!!! :)

Answer 1

Alright, what's the radius of the larger cylinder?

Answer 2

Radius of the large is 6 times greater than the smaller one, therefore radius is \(22*6=132\)

Answer 3

I got that. But i seem to be missing something.

Answer 4

Now find the volume of the small cylinder;

Height = 45cm
Radius = 22cm

\(\large V_{Cyl}=A_{Base}*\text{Height}\)
\(\large V=\pi r^2*h\)
\(\large V=\pi*22^2*45\)
\(\large V=21780\pi\)

Is that what you got?

Answer 5

Following the same formula, find the volume of the big cylinder

Height = 45cm
Radius = 132cm

\(\large V=\pi r^2*h\\V=\pi*132^2*45\\V=784080\pi\)

Answer 6

not at all

Answer 7

"What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder?"

\(\large V_{Large}=784080\pi\)
\(\large V_{Small}=21780\pi\)

\[\large \text{Ratio}=\frac{784080\pi}{21780\pi}=\frac{36}{1}\]

Answer 8

Can you show me your steps? So I can point out where are your mistakes and what you should remember the next time you'll encounter this kind of problem :)

Answer 9

My steps endedwith 22*6. i was lost. but i am reworking now to try to figure it out. thanks.

Answer 10

You are welcome, if you have any problem, just message me like you did earlier :)

Answer 11

Will do! Thanks again!!!