Volume of Prisms and Cylinders
Volume is the amount of three-dimensional space an object occupies, measured in cubic units. For prisms and cylinders, volume = area of cross-section x height.
What You Need to Know
Key Concept Diagram
Volume of any prism = area of base (cross-section) x height
Volume of a rectangular prism = length x width x height
Volume of a triangular prism = (1/2 x base x height of triangle) x length
Volume of a cylinder = pi x r^2 x height
Units of volume: mm^3, cm^3, m^3; 1 litre = 1000 cm^3
Key Vocabulary
Volume
The amount of 3D space enclosed by a solid, measured in cubic units (cm^3, m^3)
Prism
A 3D solid with two identical parallel cross-sections and rectangular side faces
Cylinder
A solid with two identical circular ends and a curved surface; volume = pi r^2 h
Cross-section
The 2D shape you see when you cut through a solid parallel to its base
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the volume of a rectangular prism with length 5 cm, width 4 cm, and height 3 cm?
Question 2
A triangular prism has a triangular face with base 6 cm and height 4 cm. The prism is 10 cm long. What is its volume?
Question 3
A cylinder has radius 3 cm and height 7 cm. What is its volume? (Use pi = 3.14)
Key Concepts Summary
- ●Volume of any prism = area of base (cross-section) x height
- ●Volume of a rectangular prism = length x width x height
- ●Volume of a triangular prism = (1/2 x base x height of triangle) x length
- ●Volume of a cylinder = pi x r^2 x height
- ●Units of volume: mm^3, cm^3, m^3; 1 litre = 1000 cm^3