Question

The surface areas 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?

Answer 1

@Lolipop_Drum312
That is not correct, nor is your method anywhere close.

Answer 2

If two figures are similar then their linear dimensions have a simple ratio

i.e. L1/L2 = some constant k (the scale factor)

Their areas are proportional to the SQUARE of the linear scale factor

Their volumes are proportional to the CUBE of the linear scale factor.

You know that the areas are in the ratio 25/36

so k^2 = 25/36 (=5^2/6^2)

So you can easily work out the scale factor k

NOW the volumes are proportional to the CUBE of this

so 250/V2 = k^3

you have worked out k from above, so solve for V2