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

Question

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Respuesta :

andromache andromache · Answer 1 · 2020-07-20T04:49:56+02:00

Answer:

A:C = 9:20

Step-by-step explanation:

The computation of the ratio is shown below:

We can say that

Surface area ratio = Ratio square

i.e

[tex](\frac{A}{B})^2 = \frac{9}{16}[/tex]

Now squaring both sides

[tex]\frac{A}{B} = \sqrt{\frac{9}{16} } \\\\ \frac{A}{B} =\frac{3}{4}[/tex]

The ratio is 3: 4

Now in the other case

Volume ratio = Cube ratio

i.e

[tex](\frac{B}{C})^3 = \frac{27}{125}[/tex]

Now cubing root both sides

So,

[tex]\frac{B}{C} = \frac{3}{5}[/tex]

Therefore

B : C = 3:5

Now for making the equivalent ratios

A:B:C = 9:12:20

So,

A:C = 9:20