Volume of Prisms and Cylinders
Base area times height.
Key idea
Base area times height.
In depth
Volume is the amount of space filled. For any prism or cylinder, V = (area of base) × height, since identical layers stack up. For a cylinder V = πr²h.
Worked example
A cylinder radius 3, height 10: V = π × 9 × 10 = 90π ≈ 283.
Formula
Real-world uses
- Calculating how much water a tank holds
- Capacity of cans and cardboard boxes
Common mistake
Using the slant edge of an oblique prism as the height. Use the perpendicular height.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Volume of Prisms and Cylinders?
Base area times height. It is a topic at the intermediate level in Geometry.
What is the formula for Volume of Prisms and Cylinders?
The key formula is V = B h.
Where is Volume of Prisms and Cylinders used in real life?
Real-world examples: Calculating how much water a tank holds; Capacity of cans and cardboard boxes.
What should I learn before Volume of Prisms and Cylinders?
Make sure you are comfortable with Cyclic Quadrilaterals, the previous topic in Geometry.
What is a common mistake with Volume of Prisms and Cylinders?
Using the slant edge of an oblique prism as the height. Use the perpendicular height.
How can I practise Volume of Prisms and Cylinders?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Volume of Prisms and Cylinders?
Move on to Surface Area of Prisms next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.