Volume of 3D Shapes
Volume measures the three-dimensional space inside a solid. Year 9 extends volume calculations to prisms, cylinders, pyramids, and cones.
What You Need to Know
Key Concept Diagram
Volume of a prism or cylinder = base area × perpendicular height
Volume of a pyramid or cone = ⅓ × base area × perpendicular height
Volume of a sphere = (4/3)πr³
Always check units: cm → cm³, m → m³; convert before calculating
Key Vocabulary
Volume
The amount of three-dimensional space enclosed by a solid, measured in cubic units
Prism
A solid with two identical parallel bases joined by rectangular faces
Pyramid
A solid with a polygonal base and triangular faces meeting at a single apex
Cone
A solid with a circular base and a curved surface tapering to a point
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A cylinder has radius 5 cm and height 10 cm. What is its volume?
Question 2
A cone has the same base radius and height as a cylinder. The cone's volume is:
Question 3
What is the volume of a sphere with radius 3 cm? (Leave in terms of π)
Key Concepts Summary
- ●Volume of a prism or cylinder = base area × perpendicular height
- ●Volume of a pyramid or cone = ⅓ × base area × perpendicular height
- ●Volume of a sphere = (4/3)πr³
- ●Always check units: cm → cm³, m → m³; convert before calculating