# Circles, Cylinders and Circular Shapes

Scheme of work: Key Stage 3: Year 8: Term 4: Circles, Cylinders and Circular Shapes

#### Prerequisite Knowledge

• Derive and apply formulae to calculate and solve problems involving: the perimeter and area of triangles, parallelograms, trapezia, the volume of cuboids (including cubes) and other prisms.
• Calculate and solve problems involving: perimeters of 2-D shapes and composite shapes.

#### Key Concepts

• The radius is the distance from the centre to any point on the circumference.  The plural radius is radii.
• The diameter is the distance across the circle through the centre.
• Ï€ is a Greek letter used to represent the value of the circumference of a circle divided by its diameter.
• The circumference is the distance about the edge of a circle. The circumference of a circle can be calculated as:
• C = ÏπD where D is the diameter, or,
• C = 2πr
• Where r is the radius.
• The area of a circle can be calculated using the formula
• A = πr2, where r is the radius.
• A cylinder is a circular prism.

#### Working Mathematically

• Develop fluency
• Use language and properties precisely to analyse numbers, algebraic expressions, 2-D
and 3-D shapes, probability and statistics.
• Use algebra to generalise the structure of arithmetic, including to formulate
mathematical relationships
• Substitute values in expressions, rearrange and simplify expressions, and solve
equations
• Reason mathematically
• Make and test conjectures about patterns and relationships; look for proofs or counterexamples.
• Begin to reason deductively in geometry, number and algebra, including using geometrical constructions
• Solve problems
• Begin to model situations mathematically and express the results using a range of
formal mathematical representations
• Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine
problems.

#### Subject Content

• Shape
• Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
• Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
• Derive and apply formulae to calculate and solve problems involving: perimeter and area of  circles and cylinders

## Circles, Cylinders and Circular Shapes  Resources

### Mr Mathematics Blog

#### Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

#### GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

#### Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.