Sheet № 100 · Foundation + Higher · AQA · Edexcel · OCR
Area of a Circle –
The area of a circle is one of the most frequently tested topics at GCSE. You need to know the formula, be confident working with both radius and diameter, and handle semicircles and quarter circles. This guide covers everything from the basic formula to reverse problems where you find the radius from a given area.
§Key definitions
Question:
A circle has a radius of 5 cm. Find its area. Give your answer to 1 decimal place.
Answer:
78.5 cm² (1 d.p.)
Q1 (Foundation):
A circle has a diameter of 12 cm. Find its area to 1 decimal place.
Q2 (Foundation):
Find the area of a quarter circle with radius 8 cm. Give your answer to 1 decimal place.
Q3 (Higher):
A semicircle has an area of 100 cm². Find its radius to 2 decimal places.
§Formulas to memorise
A = pi r², where r is the radius of the circle
Semicircle area = ½ pi r²
Quarter circle area = ¼ pi r²
Substitute the radius into A = pi r² and calculate.
Worked example
A circle has a radius of 5 cm. Find its area. Give your answer to 1 decimal place.
Working: A = pi r² A = pi × 5² A = pi × 25 A = 78.5398...
⚠ Common mistakes
- ✗Using the diameter instead of the radius. The formula uses r, not d. If you are given the diameter, divide by 2 first. Using the diameter gives an answer four times too large.
- ✗Forgetting to square the radius. Writing pi × r instead of pi × r² gives a circumference-like answer, not an area.
- ✗Rounding pi too early. Use the pi button on your calculator or keep the full value 3.14159... until the final step to avoid inaccuracy.
- ✗Forgetting to halve or quarter for parts of circles. A semicircle is half the area, a quarter circle is one quarter. Always divide after computing the full circle area.
✦ Exam tips
- →If the question says "give your answer in terms of pi", leave your answer as a multiple of pi (e.g. 25pi) and do not convert to a decimal.
- →For reverse problems (finding r from area), divide the area by pi first, then take the square root.
- →Always state your units as cm², m², etc. — area is measured in square units.