Question

Three solid shapes A,B and C are similar the surface of shape A is 9cm² the surface of shape B is 16cm² the ratio of the volume of shape B to the volume to 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

PLEASE ANSWER ASAP

Answer 1

A:C = 9:20

Explanation:

The computation of the ratio is shown below:

We can say that

Surface area ratio = Ratio square

i.e

`((A)/(B))^2 = (9)/(16)`

Now squaring both sides

`(A)/(B) = \sqrt{(9)/(16) } \\\\ (A)/(B) =(3)/(4)`

The ratio is 3: 4

Now in the other case

Volume ratio = Cube ratio

i.e

`((B)/(C))^3 = (27)/(125)`

Now cubing root both sides

So,

`(B)/(C) = (3)/(5)`

Therefore

B : C = 3:5

Now for making the equivalent ratios

A:B:C = 9:12:20

So,

A:C = 9:20