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The number of solid spheres each of diameter 6 cm, that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm is?

Correct answer: C. 5

  • A. 3
  • B. 4
  • C. 5
  • D. 6

Explanation

Each sphere has radius 3 cm, so its volume is 4/3 x pi x 3^3 = 36pi cm3. The cylinder has radius 2 cm and height 45 cm, so its volume is pi x 2^2 x 45 = 180pi cm3. Thus the number of spheres is 180pi cm3 / 36pi cm3 = 5, while 4 usually results from an arithmetic error in the sphere volume.

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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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