Similar Figures

What effect will multiplying the sides of a 3D shape by a factor of 3 have on its volume? Let's see what happens using a rectangular prism.

Rectangular Prism

First find the volume of the original shape. The volume of a prism is found by multiplying the area of the base, in this case a rectangle, by the height.

Volume = (3 × 4) × 5 = 12 × 5 = 60 cm3

If we apply a scale factor of 3 to all of the sides, we need to multiply each dimension by 3. We now have a (3 × 3) × (4 × 3) × (5 × 3)  and its volume is:

Volume of similar figure = 9 × 12 × 15 = 1620 cm3

How much larger is the new volume compared to the original volume? We can find out by taking the new volume and dividing it by the original.

1620 ÷ 60 = 27

The new volume is 27 times larger than the original when we applied a scale factor of 3. Volume is represented by cubic units and 27 is a perfect cube of 3.

 

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