Area and volume
Area-and-volume questions usually come down to choosing the right formula, converting units, and checking whether the problem asks for a length, an area, or a volume.
Core Idea
Area measures how much surface a flat shape covers; volume measures how much space a solid occupies. Most SAT geometry problems boil down to picking the right formula, plugging in carefully, and tracking your units.
Understanding
Rule: Pick the formula that matches the solid, then keep the units consistent.
- Flat shapes use area formulas; solids use surface area or volume formulas.
- Radius vs. diameter and mixed units are the usual traps.
- Scale factors change lengths, areas, and volumes at different rates.
Label the shape first and convert units before you multiply.
Concept Guides
7Solve problems involving perimeter and area of plane figures.
Perimeter adds edges; area measures the inside, and composite shapes are often split and recombined.
Solve problems involving surface area of solids (e.g., prisms, pyramids, cylinders).
Surface area is the sum of all outside faces, with special attention to slant height and whether the
Solve problems involving volume of solids (e.g., prisms, pyramids, cylinders).
Volume comes from base area times height, with cones and pyramids taking one-third of the matching p
Use scale factors to reason about changes in length and area (and volume when relevant).
Scale factors change length by k, area by k^2, and volume by k^3.
Solve for a missing dimension given area/surface area/volume information.
Use the area or volume formula to work backward from a given measure to the missing length.
Apply formulas correctly and track units.
Match the formula to the shape, use the right measurements, and keep units consistent.
Convert between units when needed (unit conversion).
Convert units before calculating area or volume, or square or cube the conversion factor if you conv