The side of a cube is elongated and becomes three times larger than its original length. The new larger cube will hold 108 liters of water. How much water can fit in the small original cube?

Question

The side of a cube is elongated and becomes three times larger than its original length. The new larger cube will hold 108 liters of water. How much water can fit in the small original cube?

Answer 1

Let "a" be the length of the side of the original cube.

3a - the length of the side of the new cube with an elongated side.

Volume of the original cube:

V_original = a³

Volume of the new cube with elongated side:

V_new = (3a)³ = 27a³

Writing the proportion:

(a³)/(27a³) = x/(108) → solving for "x"

x = 108/27 = 4 (liters of water)

Answer 2

Since the length is 3 times the original, 3 cubes would fit into the elongated one. 108/3 = 36 cubic feet.

This makes the side of each cube = (36)^(1/3) - the cubed root of 36.