Question

The radii of the bases of two similar cylinders are in

the ratio 5/1. 1 The height of the larger cylinder is 45 cm.
Calculate:
A) the height of the smaller cylinder
B) the ratio of the volumes of the two cylinders.

Answer 1

A) 9cm

B) 125:1

Explanation:

A) Height of the smaller cylinder

If the radii of two similar cylinders are in the ratio 5:1, and the height of the larger cylinder is 45 cm, then the height of the smaller cylinder should be:

(1/5) * 45 cm = 9 cm

B) The ratio of the volumes of the two cylinders

The formula for the volume V of a cylinder is indeed V = πr²h, where r is the radius and h is the height.

So, the volume of the larger cylinder (V1) is:

V1 = π*(15 cm)²*(45 cm)

And the volume of the smaller cylinder (V2) is:

V2 = π*(3 cm)²*(9 cm)

So, the ratio of the volumes V1/V2 is:

V1/V2 = (π*(15 cm)²*(45 cm)) / (π*(3 cm)²*(9 cm))

This simplifies to:

V1/V2 = (15/3)² * (45/9)

Which is:

V1/V2 = 5² * 5 = 125

So, the ratio of the volumes of the two cylinders is 125:1

:)