Scaling in Space Math Example 4

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Example 4

hard
Two similar pyramids have heights 4 m and 10 m. If the smaller pyramid has volume 3232 m³, what is the volume of the larger?

Solution

  1. 1
    Step 1: Scale factor k=10/4=2.5k = 10/4 = 2.5.
  2. 2
    Step 2: Volume ratio =k3=2.53=15.625= k^3 = 2.5^3 = 15.625.
  3. 3
    Step 3: Larger volume =32×15.625=500= 32 \times 15.625 = 500 m³.

Answer

500500 m³
For similar 3D figures, the ratio of volumes equals the cube of the ratio of corresponding lengths. Since k=2.5k = 2.5, the volume scales by 2.53=15.6252.5^3 = 15.625. This rule applies to any pair of similar 3D shapes.

About Scaling in Space

How length, area, and volume measurements change when a figure is uniformly enlarged or shrunk by a scale factor.

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More Scaling in Space Examples

Example 1 easy

A square has side length 3 cm. If all lengths are doubled (scale factor [formula]), what are the new

Example 2 medium

A sphere has radius 2 cm and volume [formula]. If the radius is tripled, how many times larger is th

Example 3 easy

A photo is 4 in × 6 in. It is enlarged with scale factor [formula]. What are the new dimensions and

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