Geometry & Trigonometry • 15% of test
Area & Volume
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Area & Volume?
Area and volume questions test formulas for 2D and 3D shapes. Most formulas are provided on the reference sheet, but familiarity speeds up problem-solving.
Step-by-Step Strategy
⚠️ Common Traps to Avoid
Frequently Asked Questions
Which formulas are provided?
Most area, volume, and special triangle formulas are on the reference sheet. Check it!
How do I find surface area?
Calculate the area of each face and add them up. For a box, that's 2(lw + wh + lh).
What's the difference between radius and diameter?
Diameter = 2 × radius. Read carefully which one the problem gives you.
How do I handle composite shapes?
Break into basic shapes, find each area or volume, then add (or subtract for holes).
Can I use Desmos for geometry?
For some problems, yes. Graph shapes on the coordinate plane to find dimensions.
Are 3D problems common?
Less common than 2D, but expect 1-2 volume or surface area questions per test.
How do I find the 'Surface Area of a Cylinder'?
Total SA = 2πr² (two bases) + 2πrh (side area). The side area is just the Circumference × Height.
What is the 'Surface Area of a Sphere'?
SA = 4πr². It is exactly four times the area of its great circle cross-section.
How does volume change if I double the radius?
Volume depends on r². Doubling radius quadruples area and octuples (8x) volume if height also doubles.
What is 'Lateral' area?
The area of the sides of a 3D shape, excluding the areas of the top and bottom bases.
How do I find the volume of an irregular prism?
Volume = Area of the Base × Height. This works for any prism as long as the cross-section is uniform.
What is the volume relationship of cones and cylinders?
A cone with the same radius and height is exactly 1/3 the volume of the containing cylinder.
How do I handle volume with different units?
Always convert dimensions to the final units BEFORE calculating to avoid complex factor errors (1 ft³ = 1728 in³).
What is the volume of a pyramid?
V = ⅓BaseArea × h. Like a cone, any pyramid is 1/3 of the volume of the corresponding straight prism.
How do I find the 'Diagonals' of a 3D box?
Use the 3D distance formula (Pythagorean extension): d² = l² + w² + h².