SAT Math: Volume of Solids
25+ practice questions in Praczo
The concept, explained
- 1
These formulas are on the SAT reference sheet: memorize which scenario uses which. Rectangular prism: V = lwh. Cylinder: V = πr²h. Cone: V = (1/3)πr²h. Sphere: V = (4/3)πr³. Pyramid: V = (1/3)Bh.
- 2
Cones and pyramids have a factor of 1/3 compared to their full-volume counterparts (cylinder, prism).
- 3
When given diameter, convert to radius before substituting into the formula.
- 4
For composite shapes (e.g., a cylinder topped by a cone), compute each volume separately and add or subtract.
- 5
The SAT often asks how volume changes when one dimension is scaled — e.g., if radius doubles, volume quadruples (since r is squared).
- ✗ Using diameter instead of radius in the formula (especially for spheres and cylinders).
- ✗ Forgetting the 1/3 factor for cones and pyramids.
SAT-style practice
A cone has a base radius of 3 and a height of 4. What is its volume?
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