Question

One cube-shaped container has an edge length 2 cm longer than the edge length of a second cube. The volume of the larger cube is 729 cm³. When the larger cube empties into the smaller cube, how much water will spill?

A. 27 cm³
B. 64 cm³
C. 125 cm³
D. 0 cm³

Answer 1

When the larger cube empties into the smaller cube, no water will spill because the volumes are the same.

Step-by-step explanation:

To find the amount of water that spills when the larger cube empties into the smaller cube, we need to compare their volumes.

The volume of the larger cube is given as 729 cm³. Let's assume the edge length of the smaller cube is x cm.

Since the edge length of the larger cube is 2 cm longer than the edge length of the smaller cube, the edge length of the larger cube is x + 2 cm.

Using the formula for the volume of a cube, we can equate the volumes of the two cubes and solve for x: (x + 2)³ = 729.

Simplifying this equation, we find that x = 9 cm.

Therefore, the volume of the smaller cube is 9³ = 729 cm³.

When the larger cube empties into the smaller cube, no water will spill because the volumes are the same. So the answer is D. 0 cm³.