Question

the surface area of two similar figures are 25 in ^2 and 36 in ^2 if the volume of the smaller figure is 250 in ^3 then what is the volume of the larger figure?

Answer 1

432 in^3

Explanation:

The ratio of linear dimensions is the square root of the ratio of the areas, so is ...

scale factor = √(36/25) = 6/5

The ratio of volumes is the cube of the ratio of linear dimensions, so is ...

volume ratio = (scale factor)^3 = (6/5)^3 = 216/125

Then the volume of the larger figure is ...

larger volume = (250 in^3)·(216/125) = 432 in^3