A lead sphere with a diameter of 3 cm is melted and reshaped into three smaller spheres. If the diameters of two of these smaller spheres are 1.5 cm and 2 cm, what is the diameter of the third sphere?

Explanation

The volume of the original sphere is equal to the sum of the volumes of the three smaller spheres. Using the formula for the volume of a sphere (4/3 π r³), calculate the radius of the third sphere. Given diameters 1.5 cm and 2 cm, their volumes are (4/3)π(0.75)³ and (4/3)π(1)³ respectively. Subtracting these from the original volume and solving for the radius of the third sphere yields a radius of 1.25 cm, so the diameter is 2.5 cm.