Area & Volume

Unit 4 · Geometry & Trigonometry

What the SAT asks here

The Digital SAT provides a reference sheet at the start of every Math section that lists the standard area and volume formulas, so you don't need to memorise them — you need to apply them. About one problem per test, often involving composite figures or working backward from a known area or volume.

2D area (on the SAT reference sheet)

Rectangle

A = \ell w

Triangle

A = \tfrac{1}{2} b h

Circle

A = \pi r^2

Trapezoid

A = \tfrac{1}{2}(b_1 + b_2) h

3D volume (on the SAT reference sheet)

Rectangular prism

V = \ell w h

Cylinder

V = \pi r^2 h

Sphere

V = \tfrac{4}{3} \pi r^3

Cone

V = \tfrac{1}{3} \pi r^2 h

SAT Tip: For composite figures, decompose into shapes you know, then add or subtract their areas (or volumes). Sketch even if the problem doesn't include a figure.

Caution: Always confirm whether the problem gives you the radius or the diameter — many SAT distractors come from using the wrong one.

Type 1

Direct application

Plug the given dimensions into the appropriate formula and simplify. Leave π in the answer when the problem asks for the exact form.

Example 1

A cylindrical water tank has radius 3 ft and height 8 ft. Find its volume in cubic feet (exact, in terms of π).

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Type 2

Composite figure

Decompose the figure into shapes you have formulas for, then add or subtract their areas (or volumes).

Example 2

A rectangle measures 10 by 6. A semicircle of diameter 6 is cut out from one short side. Find the remaining area, in terms of π.

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Type 3

Work backward from a known volume or area

Solve the formula for the unknown dimension. Cube roots come up for cube volumes; square roots for square areas.

Example 3

A cube has volume 125 cubic inches. Find the length of one edge.

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