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A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is_________?

Correct answer: D. 1: 3

  • A. 3: 5
  • B. 2: 5
  • C. 3: 1
  • D. 1: 3

Explanation

The cylinder volume is pi x r^2 x h_c, while the cone volume is 1/3 x pi x r^2 x h_n. Equal volumes and equal radii give h_c = h_n/3, so the height ratio is h_c:h_n = 1:3. The likely wrong choice is 3:1, which reverses the ratio being asked for.

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About Area and Volume

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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