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The radius of a circular cylinder is the same as that of a sphere. Their volumes are equal. The height of the cylinder is________?

Correct answer: A. 4/3 times its radius

  • A. 4/3 times its radius
  • B. 2/3 times its radius
  • C. Equal to it's radius
  • D. Equal to it's diameter

Explanation

Equal volumes give pi x r^2 x h = 4/3 x pi x r^3, where r is the common radius. Cancelling pi x r^2 gives h = 4r/3, so the cylinder height is 4/3 times its radius. The likely mistake is choosing the diameter, 2r, by using the sphere's diameter instead of equating volumes.

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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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