Calculate the area of two-dimensional shapes and the volume of three-dimensional solids.
49 original area and volume questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
A closed rectangular box has length 5, width 4, and height 3. What is the total surface area of the box?
Surface area is 2(lw + lh + wh) = 2(5·4 + 5·3 + 4·3) = 2(20 + 15 + 12) = 2(47) = 94. Choice 60 is the volume (5 · 4 · 3); choice 47 forgets to double the sum of the three face areas.
A rectangle has a length of 10 and a width of 9. What is its area?
Area is length times width: 10 × 9 = 90. The classic slip is adding instead of multiplying: 10 + 9 = 19, and 19 is sitting in the choices waiting for it. The other wrong answers are near-miss products with one side off by one, so a quick times-table check catches them. (If a question asks for perimeter instead, that is 2 × (10 + 9) = 38.)
A rectangle has a length of 2 and a width of 4. What is its area?
Area is length times width: 2 × 4 = 8. The classic slip is adding instead of multiplying: 2 + 4 = 6, and 6 is sitting in the choices waiting for it. The other wrong answers are near-miss products with one side off by one, so a quick times-table check catches them. (If a question asks for perimeter instead, that is 2 × (2 + 4) = 12.)
A rectangle has a length of 10 and a width of 3. What is its area?
Area is length times width: 10 × 3 = 30. The classic slip is adding instead of multiplying: 10 + 3 = 13, and 13 is sitting in the choices waiting for it. The other wrong answers are near-miss products with one side off by one, so a quick times-table check catches them. (If a question asks for perimeter instead, that is 2 × (10 + 3) = 26.)
A rectangle has a length of 3 and a width of 12. What is its area?
Area is length times width: 3 × 12 = 36. The classic slip is adding instead of multiplying: 3 + 12 = 15, and 15 is sitting in the choices waiting for it. The other wrong answers are near-miss products with one side off by one, so a quick times-table check catches them. (If a question asks for perimeter instead, that is 2 × (3 + 12) = 30.)