Answer:
- 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.