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"Scaling Area" Explained

When scaling area, the scale factor is multiplied twice or squared.

Key Idea: Scaling Area

When a figure is scaled, its area changes according to the square of the scale factor.

General Rule:

  • If the linear scale factor is k=, the area scale factor is k^2.

  • Formula:

New Area = (Scale Factor)^2×Original Area

  • Doubling a shape’s sides makes its area four times larger; tripling makes it nine times larger, etc.

Why this matters for the SAT:

Scaling problems appear in geometry, especially with similar figures.
Recognizing that area scales with the square of the linear factor prevents mistakes and allows quick calculations of new areas.

"Scaling Volume" Explained

When scaling volume, the scale factor is multiplied three times or cubed.

Key Idea: Scaling Volume

When a 3D figure is scaled, its volume changes according to the cube of the linear scale factor.

General Rule:

  • If the linear scale factor is k, the volume scale factor is k^3.

  • Formula:

New Volume = (Scale Factor)^3 × Original Volume
Doubling a figure’s sides makes its volume eight times larger; tripling makes it 27 times larger, etc.

Why this matters for the SAT:

Scaling volume is common in geometry and word problems involving similar 3D shapes.
Knowing that volume scales with the cube of the factor allows quick and accurate calculations.