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Three solid shapes a, b and c are similar.
the volume of shape a is 27 cm
the volume of shape b is 64 cm
the ratio of the surface area of shape b to the surface area of shape c is 8:15
work out the ratio of the height of shape a to the height of shape c.

Respuesta :

jayilych4real

The ratio of the height of shape A to the height of shape C is [tex]\frac{3}{10}[/tex]

Calculations and Parameters:

First step:

Recall that similar figures have the same scale factor squared due to the ratio of its surface area.

Hence,

We would make:

  • z-----> the scale factor
  • x----> surface area shape A
  • y----> surface area shape B

[tex]z^2 = x/y\\z= 2/5[/tex]

Therefore, the ratio of the height of shape A to the height of shape B is = [tex]\frac{hA}{hB} = \frac{2}{5}[/tex]

Next step:

To find the ratio of the height of shape B to the height of shape C, we would perform a similar operation which is:

[tex]z^3 = 27/64\\z= 3/4[/tex]

The ratio is:

[tex]\frac{hB}{hC} = \frac{3}{4}[/tex]

Final step:

To find the ratio of the height of shape A to the height of shape C would be:

[tex](\frac{hA}{hB}) (\frac{hB}{hC} )= \frac{hA}{hC}[/tex]

= 6/20

= 3/10

Read more about the ratios here:

https://brainly.com/question/12357318

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