The surface area of two similar figures are 25in^2 and 36in^2 If the volume of the smaller figure is 250in^3 what is the volume of the larger figure.

Question

The surface area of two similar figures are 25in^2 and 36in^2   If the volume of the smaller figure is 250in^3 what is the volume of the larger figure.

mathstudent55 · Answer

If two similar figures have a scale factor of s, or a ratio of s/1 then
the surface areas of the similar figures is in a ratio of s^2/1, and 
the volumes of the figures are in a s^3/1 ratio.

jhannybean · Answer

The key is to understanding the relationship between the measurement of volume and area.

mathstudent55 · Answer

The area scale factor is

$s^2 = \dfrac{36}{25}$

Taking the square root of both sides, the linear scale factor is:

$s = \dfrac{6}{5} $

The volume sale factor is:

$ s^3 = (\dfrac{6}{5})^3 = \dfrac{216}{125}$

$250~in.^3 \times \dfrac{216}{125} = 432~in.^3 $

mathstudent55 · Answer

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