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Surface area of two spheres are in the ratio 1:4 what is the ratio of their volumes?

Correct answer: B. 1:8

  • A. 1:64
  • B. 1:8
  • C. 1:4
  • D. 8:1

Explanation

Sphere surface area is proportional to r^2, so a surface-area ratio of 1:4 gives a radius ratio of 1:2. Sphere volume is proportional to r^3, hence the volume ratio is 1^3:2^3 = 1:8. The likely wrong choice is 1:4, which copies the surface-area ratio without taking the cube relationship.

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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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