Three solid shapes, A, B and C are similar.

The surface area of shape A is 9cm^2

The surface area of shape B is 16cm^2

The ratio of the volume of shape B to the volume of shape C is 27 : 125

Work out the ratio of the height of shape A to the height of shape C.

Give your answer in its simplest form.

A:C = 9:20

Step-by-step explanation:

The ratio of the surface area of similar solid is equal to the square of the ratio of their corresponding linear measures. If the ratio of their corresponding linear measures is a:b, the surface area ratio will be (a/b) ². Therefore,

(A/B) ² = 9/16

square root both sides

A/B = √9/√16

A/B = 3/4

A:B = 3:4

The ratio of volume of two similar solid is the ratio cube of their corresponding linear measures. Therefore,

(B/C) ³ = 27/125

cube root both sides

B/C = 3/5

B:C = 3:5

To make the ratio equivalent

A:B:C = 9:12:20

A:C = 9:20