Question

The sides of two cubes differ by 2 cm and their volumes differ

Answer 1

The length of the side of the smaller cube is 3.48cm

• Let the length of the smaller side be x
• The length of the bigger side will be x + 2

• Volume of the smaller cube  = x^3
• Volume of the larger cube  = (x+2)^3

If their volumes differ  by 152 cm^3, then;

x^3 - (x+2)^3 = 153

Expand

x^3 - (x^3 + 3x^2(2^2) + 3x(2^3) + 2^4) = 153

x^3-x^3-12x^2-24x + 16 = 153

-12x^2-24x + 16 = 153

12x^2 + 24x - 16 - 153 = 0

12x^2 + 24 -169 = 0

On factorizing, the value of x is 3.48. This shows that the length of the side of the smaller cube is 3.48cm

Learn more on volume of cubes here:  brainly.com/question/1972490