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The height of two right circular cones are in the ratio 1:2 and their perimeters of their bases are in the ratio 3:4, the ratio of their volume is_________?

Correct answer: C. 9:32

  • A. 3:8
  • B. 9:16
  • C. 9:32
  • D. 9:64

Explanation

The base perimeter is proportional to the radius, so the radii are in the ratio 3:4. Since cone volume is proportional to r^2h, the volume ratio is 3^2 x 1 : 4^2 x 2 = 9:32. The likely mistake is 9:16, which uses the radius-squared ratio but forgets that the second cone has twice the height.

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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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