Would you rather have a cube of gold that measures

25 mm on each side, or two cubes of gold, one is 24 mm per side, and one is 7 mm per side?

Whichever option you choose, justify your reasoning with mathematics. Show/Type your work.

Cube of side 25 mm

Explanation:

Dimension of cube:

Side, a = 25mm

Volume of cube = (a) ³

V = (25mm) ³

V = 15625 mm³

Dimension of smaller cube:

Side, a₁ = 24 mm

side a₂ = 7mm

Volume of cube with side 24mm

V = (24) ³

V = 13824 mm³

Volume of cube with side 7mm

V = (7mm) ³

V = 343 mm³

Total volume of two smaller cubes = 13824 + 343 mm³

= 14167 mm³

Since the volume of bigger cube of side 25mm³ is greater than the two smaller cubes of side 24mm and 7mm, I would rather have a cube of gold that measures 25 mm on each side.