Question

What happens to the surface area and volume if the lengths of the dimensions of the

prism are multiplied by a scale factor of 3?

Answer 1

• area is multiplied by 9
• volume is multiplied by 27

Explanation:

Area of a scaled figure is multiplied by the square of the scale factor; volume is multiplied by the cube of the scale factor.

Area

When dimensions are multiplied by 3, the area is multiplied by 3² = 9.

Area of the larger figure is 9 times that of the smaller one.

Volume

When dimensions are multiplied by 3, the volume is multiplied by 3³ = 27.

Volume of the larger figure is 27 times that of the smaller one.

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Additional comment

In general, the area of a figure is the sum of the products of two orthogonal dimensions. If each of those is multiplied by 3, then the product is multiplied by 3 twice, or 3² = 9.

Similarly, the volume of a figure is the sum of products of three orthogonal dimensions. When those are each multiplied by 3, the product is multiplied by 3 three times, or 3³ = 27.