The surface areas of two similar solids are 441 cm2 and 225 cm2. If the approximate volume of the smaller solid is 250 cm3, what is the volume of the larger solid?

volume of the larger solid = 686 cm³

Step-by-step explanation:

The solids are similar. A solid is similar if all the corresponding sides are proportional. They are similar if they are the same type of solids and their corresponding sides like height, radius etc are proportional.

The ratio of the surface area of a similar solid is equal to the square of their scale factor.

(a/b) ² = 441/225

square root both sides

a/b = √441/√225

a/b = 21/15

The ratio of the volume of a similar solid is equal to the cube of their scale factor. Therefore,

(21/15) ³ = a/250

9261 / 3375 = a/250

cross multiply

9261 * 250 = 3375a

2315250 = 3375a

divide both sides by 3375

a = 2315250/3375

a = 686 cm³

volume of the larger solid = 686 cm³