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The spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls. The diameters of two of these are 1 ½ cm and 2 cm respectively. The diameter of third ball is?

Correct answer: B. 2.5 cm

  • A. 2.66 cm
  • B. 2.5 cm
  • C. 3 cm
  • D. 3.5 cm

Explanation

For spheres, volume is proportional to the cube of the diameter, so 3³ cm³ = (1.5 cm)³ + (2 cm)³ + d³. Hence d³ = 27 cm³ - 3.375 cm³ - 8 cm³ = 15.625 cm³, and d = 2.5 cm. The likely wrong choice is 3 cm, which ignores that some volume has already gone into the other two balls.

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Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.

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