Question

The volumes of two similar solids are 729 m^3 and 125m^3. The surface area of a larger solid is 324 m^3. What is the surface area of the smaller solid

Answer 1

Answer:

100 m^2

Step-by-step explanation:

The scale factor of the volume of solids is the cube of the scale factor of linear dimensions.

The scale factor of the area of solids is the square of the scale factor of the linear dimensions.

Volume scale factor:

125/729 = (5/9)^3

Linear scale factor:

5/9

Area scale factor:

(5/9)^2 = 25/81

Proportion to find the area of the smaller one:

Let the area of the smaller one equal x.

25/81 = x/324

81x = 25 * 324

Divide both sides by 81

x = 25 * 4

x = 100

Answer: 100 m^2