A ball with a radius of 10 cm was cut into two equal parts and 4 identical balls were melted

A ball with a radius of 10 cm was cut into two equal parts and 4 identical balls were melted from half. find the radius of one of these balls.

Let’s calculate the volume of the whole, not sawn ball.

V = 4 * π * r³ / 3 = 4 * π * 103/3 = 4000 * π / 3 cm3.

Then the volume of half of the ball is: V1 = V / 2 = (4000 * π / 3) / 2 = 2000 * π / 3 cm3.

The volumes of the four fused balls will be equal: (2000 * π / 3) / 4 = 500 * π / 3 cm3.

Let us express the radius of the cast balls in terms of their volume.

r³ = 3 * V / (4 * π) = 1500 * π / 3 * (4 * π) = 125.

r = ∛125 = 5 cm.

Answer: The radius of the molten ball is 5 cm.