Area, Surface Area & Volume — Year 8 Revision Notes
These notes cover the circumference and area of circles, the area of compound shapes, and the volume and surface area of prisms — all at Year 8 (Stage 8) level.
Circumference and area of a circle
The circumference is the distance around a circle, found with C = πd, where d is the diameter. The area is found with A = πr², where r is the radius. Remember the diameter is twice the radius. Use the π button on your calculator, or 3.14 if told to.
Key Facts & Formulas
- C = πd
- A = πr²
- d = 2r
Tips
- Diameter for circumference, radius for area.
- Square only the radius in πr², not the whole expression.
Compound area
A compound shape is made from simpler shapes joined together. Split it into rectangles, triangles or parts of circles, find each area separately, then add them — or subtract for a hole. Label each piece so you do not miss one.
Key Facts & Formulas
- Area of rectangle = length × width
- Area of triangle = ½ × base × height
Tips
- Split the shape with clear dividing lines.
- Add areas for pieces joined on, subtract for cut-outs.
Volume and surface area of prisms
The volume of a prism is the area of its cross-section multiplied by its length: V = cross-sectional area × length. For a cylinder this is V = πr²h. The surface area is the total area of all the faces; for a cuboid that is 2(lw + lh + wh). Work out each face, then add them up.
Key Facts & Formulas
- V = cross-section area × length
- Cylinder V = πr²h
- Cuboid surface area = 2(lw + lh + wh)
Tips
- Volume is measured in cubic units (cm³).
- Check you have counted every face for surface area.
Revision Checklist
- I can find the circumference and area of a circle
- I can find the area of a compound shape
- I can find the volume of a prism, including a cylinder
- I can find the surface area of a cuboid
Frequently Asked Questions
What units should I use for area and volume?
Area is two-dimensional, so it uses square units such as cm². Volume is three-dimensional, so it uses cubic units such as cm³. Mixing them up is a common way to lose marks.
Build strong foundations in Area, Surface Area & Volume
A free trial class with Teacher Rig helps your Year 8 child master Area, Surface Area & Volume now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Area, Surface Area & Volume develops in IGCSE Mensuration (Cambridge 0580) →