Volume of Prisms and Cylinders
Volume = base area × height.
About this topic
The volume of a prism or cylinder is the area of its base multiplied by its height: V = Bh. For a rectangular box this is lwh, and for a cylinder it is πr²h. Volume is measured in cubic units and describes how much the solid holds.
The formula works because the solid is made of stacked identical layers. It applies even to tilted (oblique) prisms, as shown by Cavalieri's principle. Tanks, pipes and cans use these formulas.
Worked example: a cylinder has radius 3 cm and height 10 cm. Its volume is π(9)(10) = 90π ≈ 282.7 cubic cm, or about 283 millilitres, since 1 cubic cm equals 1 mL. A box of 4 by 5 by 6 holds 120 cubic units. A triangular prism with base area 12 and height 7 has V = 84.
Water tanks, soup cans and swimming pools are volume problems. The key mistake is mixing the height of a triangular base with the height of the prism, so label them differently. Another is using diameter as radius. Remember that doubling the radius of a cylinder multiplies volume by four, while doubling the height only doubles it. Make sure to convert units before computing, since 1 cubic metre equals 1,000 litres, and give answers in cubic units.
Key ideas
- Cylinder V = πr²h
- Measured in cubic units
- Cavalieri's principle explains why
Quick check
Use cases: where Volume of Prisms and Cylinders helps
- Homework: review the key idea behind Volume of Prisms and Cylinders before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Volume of Prisms and Cylinders without notes.
- Visual learning: play with the interactive lab to see how Volume of Prisms and Cylinders changes when you adjust its inputs.
- Teaching a friend: explain Volume of Prisms and Cylinders in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Volume of Prisms and Cylinders?
Volume = base area × height.
What will I learn in Volume of Prisms and Cylinders?
Cylinder V = πr²h. Measured in cubic units. Cavalieri's principle explains why.
Is Volume of Prisms and Cylinders part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Volume of Prisms and Cylinders lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Volume of Prisms and Cylinders?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
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