lesson
Radius and diameter are not interchangeable
1 · Learn
A circle's circumference is 2πr or πd, because diameter d = 2r. Its area is πr². The first measures a boundary length, while the second measures a region. Keep π for an exact form when requested.
A calculator approximation should be rounded at the final stage. A semicircle's perimeter includes the straight diameter as well as the curved half-circumference.
2 · Worked example
For radius 5 cm, circumference is 10π cm and area is 25π cm². A semicircle of that radius has perimeter 5π + 10 cm.
3 · Your turn
Find exact circumference and area for radius 3 cm.
Check your answer
6π cm and 9π cm².
4 · Apply your learning
Draw and label the radius and diameter before choosing the formula, then distinguish exact and rounded forms.
Adult guidance and safety
Ask for the reasoning and a check, not only a numerical result. Supply accurate diagrams, coordinate grids and data displays where required. Use varied examples and revisit prerequisite gaps; these short teaching models are not a completed assessment programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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