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A solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is h. If the total volume of the solid is three times the volume of the cone then the height of the cylinder is________?

Correct answer: C. 2h/3

  • A. 2h
  • B. 4h
  • C. 2h/3
  • D. 3h/2

Explanation

Let the common base radius be r and the cylinder height be H. The cone volume is (1/3)πr^2h, while the cylinder volume is πr^2H; since total volume is three cone volumes, the cylinder is two cone volumes, giving πr^2H = (2/3)πr^2h and H = 2h/3. The likely wrong choice is 2h, obtained by ignoring the cone's factor of 1/3.

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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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