The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
Correct answer: B. 1:27
- A. 27:1
- B. 1:27
- C. 1:9
- D. 9:1
Explanation
Sphere volume is proportional to the cube of its radius, V = 4/3 pi r3. Thus radii 1:3 give volumes 1 cubed:3 cubed = 1:27. The likely alternative is 1:9, option c, which uses the square relation for surface area instead of the cube relation for volume.
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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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