Question

MEDAL!


Find the ratios of volume of cylinder A to cylinder B.
a) Cylinder A has the same radius but twice the height of cylinder B.
b) Cylinder A has the same height but twice the radius of cylinder B.

Answer 1

@satellite73 @jim_thompson5910 @amistre64

Answer 2

do you have an idea of what it is?

Answer 3

Let's make up some numbers that fit the description in part (a)

" Cylinder A has the same radius but twice the height of cylinder B."

so let's say

Cylinder A has radius r = 2, height h = 8
Cylinder B has radius r = 2, height h = 4

what is the volume of each cylinder?

Answer 4

So the formula to find the volume of a cylinder is V=Bh where B is the area of the base.

Area of circle = \[\pi \times r^2\]

Answer 5

The radius of cylinder A is 2 so
\[\pi \times 2^2\]
is about 12.56

12.56 times height = 100.48

Answer 6

The radius of cylinder B is 2, but this time the height is different so:
12.56 times 4 = 50.24

Answer 7

This seems to be that the volume of cylinder A is twice as much as the volume of cylinder B.

Answer 8

very good

Answer 9

So is it 2:1?

Answer 10

Let's prove that using variables instead of numbers. So we can show that it is true in general no matter what r or h is

Let r be the radius of both cylinders. Let h be the height of cylinder B. Cylinder A is twice as high, so its height is 2h

Answer 11

Volume of Cylinder A

V1 = pi*r^2*(2h)

Volume of Cylinder B

V2 = pi*r^2*(2h)

divide the two volumes (V1/V2)