Question

Two cylinders. The smaller cylinder has height labeled as 1 cm. The larger cylinder has height labeled as 3 cm.

The cylinders are similar. The volume of the larger cylinder is 2106 cubic centimeters. What is the volume of the smaller cylinder?



93 cm3


81 cm3


78 cm3


65 cm3

Answer 1

The correct answer is C

EXPLANATION

We have that, the smaller cylinder has height 1 cm and the larger cylinder has height 3cm.

The scale factor of similarity is

`k = (1)/(3)`

That's if the smaller cylinder is the image.

The volume of the larger cylinder is 2106 cm³.

To find the volume of the smaller cylinder, we multiply the volume of the larger cylinder by k³

`( { (1)/(3) })^(3) * 2106 {cm}^(3)`

`{ (1)/(27) } * 2106 = 78 {cm}^(3)`

Answer 2

Answer: third option.

Explanation:

You know that the height of the smaller cylinder is 1 cm and the height of the larger cylinder is 3 cm, then you can find the volume ratio. This is:

`Volume\ ratio=((1\ cm)/(3\ cm))^3\\\\Volume\ ratio=(1)/(27)`

Knowing that the volume of the larger cylinder is 2,106 cubic centimeters, you need to multiply it by the volume ratio to find the volume of the smaller cylinder.

Therefore:

`V_(smaller)=(1)/(27)(2,106\ cm^3)\\\\V_(smaller)=78\ cm^3`