Question

A cube with a side length of 10 centimeters is filled with water. A stone that just fits into the cube is submerged into it, displacing some of the water. The stone is nearly spherical. Once that stone is removed from the cube, how much water remains in the cube? Aprroximate your answer to the nearest tenth using 3.14 for pi​

Answer 1

Explanation:

The volume of the cube is given by 10^3 = 1000 cubic centimeters. Since the stone just fits into the cube, its diameter is 10 centimeters, and its radius is 5 centimeters. The volume of a sphere is (4/3)πr^3, so the volume of the stone is (4/3)π(5^3) = 523.6 cubic centimeters (approx).

When the stone is submerged in water, it displaces its own volume of water, which is equal to the volume of the stone. So the amount of water that remains in the cube after the stone is removed is the volume of the cube minus the volume of the stone, which is:

1000 - 523.6 = 476.4 cubic centimeters (approx)

Therefore, approximately 476.4 cubic centimeters of water remain in the cube.