Question

The ratio of the heights of two similar cylinders is 1:3. If the volume of the smaller cylinder is 67cm^3, find the volume of the larger cylinder. (Create two proportions, set them equal to each other and solve for x)

Answer 1

• 1809 cm³

Explanation:

Given the scale factor:

• k = h/H = 1/3

Since the cylinders are similar, the other dimensions should have same scale factor of 1/3.

The volumes are:

• v = 67 cm³
• V = x

Ratio of volumes is the cube of the scale factor, as the volume is the product of 3 dimensions:

• v/x = k³
• 67/x = (1/3)³
• x = 67*27
• x = 1809 cm³