Question

The surface areas of two similar figures are 25 in. squared and 36 in. squared. If the volume of the smaller figure is 250 in. cubed, what is the volume of the larger figure?

Thank you!

Answer 1

First, we calculate for the ratio of the surface areas of the given figures. From the given above, the ratio is equal to 25:36

Then, we calculate for the ratio of the perimeters or sides of the figures by getting the square root of the ratio in item 1.
ratio of perimeter or side = 5:6


The ratio of the volumes of the figures is equal to the cube of the ratio in item 2.
ratio of volumes = (5:6)³ = 125:216

Using this ratio and the volume of the smaller figure,
250 in³/x in³ = 125/216

The value of x from the equation is 432. Therefore, the volume of the larger figure is 432 in³.