# Area and Volume on the SAT: Examples & Practice | 1600.now Source: https://1600.now/sat-skill/area-and-volume --- Math · Geometry and Trigonometry ## Area and Volume Choose the formula for the requested quantity, then identify its perpendicular height and units. Length scales directly; area scales with the square; volume scales with the cube. Written by [Luke Finigan](https://1600.now/about) 2 min read Updated Oct 2, 2026 ### Use the perpendicular height in an area formula A triangle with base 12 and perpendicular height 5 has area $A=\frac12(12)(5)=30$ square units. A slanted side of length 13 is not the height unless it is perpendicular to the chosen base. For a parallelogram, use $A=bh$ with the same perpendicular-height rule. For a rectangle, adjacent sides supply base and height because they meet at a right angle. ### Match the solid to the volume formula A cylinder of radius 3 and height 8 has volume $V=\pi r^2h=72\pi$ cubic units. If a problem instead gives diameter 6, divide by 2 before squaring. A cone with the same radius and height has one-third that volume: $V=\frac13\pi r^2h=24\pi$. The factor belongs to the solid's formula, not to its radius or height alone. ### Use scale factors in the correct dimension If every length of a figure is multiplied by 2, its area is multiplied by $2^2=4$ and its volume by $2^3=8$. If two similar solids have volumes in the ratio $27:8$, their length ratio is $3:2$. The phrase "every length" matters. Doubling only a cylinder's height doubles its volume; doubling only its radius quadruples its volume. Do not apply a full similarity rule to a one-dimension change. ### Keep exact values until the requested rounding If the answer is requested in terms of $\pi$, leave $72\pi$ rather than replacing it with a decimal. If the question requests a rounded number, round after the final calculation. Check units at the end. An area answer should use square units and a volume answer cubic units. A leftover length unit can reveal a missing factor in the setup. ### Check your understanding Try it yourself Two similar solids have a length scale factor of 3 from the smaller to the larger. What is the volume scale factor? A $3$ B $6$ C $9$ D $27$ ### Sample area and volume questions Area and Volume · Easy The base of a triangle is 8 inches long, and the triangle's height is 11 inches. What is the area, in square inches, of the triangle? A 19 B 44 C 57 D 88 - [Open the question and explanation](https://1600.now/bank/math/197a23dd) Area and Volume · Easy A triangle has a base length of 54 centimeters and a height of 84 centimeters. What is the area, in square centimeters, of the triangle? A 2,268 B 1,134 C 4,536 D 138 - [Open the question and explanation](https://1600.now/bank/math/d953f526) Area and Volume · Easy The number of beavers in a 136-acre preserve is estimated to be 2,448. What is the estimated population density, in beavers per acre, of this preserve? A 18 B 136 C 154 D 2,466 - [Open the question and explanation](https://1600.now/bank/math/74762384) ### Practice this skill 1. Sketch and label the base, perpendicular height, and radius. 2. Write the formula before substituting numbers. 3. Include a scale-factor problem and a change-in-one-dimension problem. [Practice area and volume](https://1600.now/bank/math/skill/Area%20and%20volume) [Print the area and volume worksheet and worked answers](https://1600.now/sat-area-and-volume-worksheet). Then use a [mixed practice module](https://1600.now/modules) to check whether you can choose this method among other question types. ### Source and question labels The bank label for this guide is "Area and volume" in Geometry and Trigonometry. The worked examples above are written for this guide. - [College Board: Types of Math tested](https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types) ### Related skills - **[Circles](https://1600.now/sat-skill/circles)** Read a circle's radius before using area or circumference. - **[Lines, Angles, and Triangles](https://1600.now/sat-skill/lines-angles-triangles)** Name the geometric relationship before writing an equation. - **[Ratios, Rates, and Proportions](https://1600.now/sat-skill/ratios-rates-proportions)** Keep the compared quantities in a fixed order and write their units.