PSAT Data — converting square and cubic units

Units are part of the first skill College Board lists for Problem-Solving and Data Analysis on the PSAT/NMSQT: ratios, rates, proportional relationships and units. The unit problems that catch students most often are not the linear ones but the conversions of area and volume, where the length factor has to be squared or cubed. A square yard is 9 square feet, not 3; a cubic yard is 27 cubic feet; a square meter is 10,000 square centimeters. This material practices only those conversions, in the kinds of measurement and cost problems the test sets in context.

Each of the twelve quiz questions offers the answer you get with the linear factor, or by converting in the wrong direction, among its options, and every explanation shows which factor the conversion needs. The problems: a room's floor in square yards for carpet sold by the square yard, and the cost of carpeting another room at 30 dollars per square yard; the number of 6-inch tiles for a floor measured in feet; the cubic yards of concrete for a slab whose thickness is given in inches; the liters in a fish tank measured in centimeters and in a pool measured in meters; a wall panel in square centimeters and a park in square meters; the mass of an aluminum block whose volume is in cubic meters while the density is per cubic centimeter; the time to fill a tank from a flow rate in liters per second; a field's real area from a map scale; and a box measured in inches converted to cubic feet.

The flashcards list each conversion fact, from 144 square inches in a square foot to 1,000 liters in a cubic meter, together with the two rules behind all of them: square the length factor for area, cube it for volume.

The printable written work has eight open problems: carpet for a 14-by-11-foot room, gravel for a driveway bought in whole cubic yards, an aquarium's capacity in liters, a painting's area in square meters with the reason for dividing by 10,000, a tank in gallons given the size of a gallon in cubic inches, a floor plan's area found two ways, the mass of a wooden block, and an explanation of why a cubic yard is not 3 cubic feet.

The oral exam asks one question at a time and asks you to say the factor before you use it.

The material complements the category's existing practice on linear rates and units, which it does not repeat. All situations are invented for practice, and nothing is taken from any published test.

• Square the length factor to convert area units and cube it to convert volume units
• Convert between square inches, square feet and square yards, and between cubic inches, cubic feet and cubic yards
• Convert between square centimeters, square meters and square kilometers
• Convert volumes to capacity: cubic centimeters to milliliters and liters, cubic meters to liters
• Combine an area or volume conversion with a price, a density or a flow rate
• Find real areas from a map or plan scale
• Check the direction of a conversion: a larger unit gives a smaller number

Practice material written by Zestly, based on the PSAT/NMSQT Math skill "Ratios, rates, proportional relationships, and units" as described in College Board's Fall 2026 PSAT/NMSQT Student Guide and the Assessment Framework for the Digital SAT Suite (version 3.01, August 2024). All situations are invented. Zestly is not affiliated with College Board.