1.9 Rational and irrational numbers
Perimeter, area and volume
Everything on perimeter, area and volume that can come up in the WJEC GCSE Mathematics and Numeracy, in all three units. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
Practise perimeter, area and volume free
A worked example
Exact answers with π · [1 mark]
Find the exact area of a circle with radius 9 cm. Give your answer in terms of π.
- B181π cm²
The exam skills (13)
Area
- Rectangle: length × width. Triangle: ½ × base × height.
- Parallelogram: base × height. Trapezium: ½(a + b)h.
- Use the perpendicular height and give units squared.
Watch out: Using the sloping side instead of the perpendicular height.
Area of a circle
- Area = πr². Circumference = πd.
- If you are given the diameter, halve it for the radius.
- Round at the end, with units.
Watch out: Using the diameter in πr².
Volume
- Volume = length × width × height.
- Make sure all the lengths are in the same units.
- Give units cubed: cm³.
Watch out: Giving units squared.
Compound perimeter
- Work out any missing sides from the ones you know.
- Go round the shape, adding every side once.
- Count the sides: an L shape has six.
Watch out: Missing out the two sides you had to work out.
Exact answers with π
- Use the formula as normal, but leave π as a letter.
- Work out the numbers: π × 2² = 4π.
- Write the number in front of π.
Watch out: Typing π into the calculator. "In terms of π" means keep the π.
Area of a sector
- A sector is a fraction of a circle: angle/360.
- Area = angle/360 × πr². Arc length = angle/360 × πd.
- Round at the end.
Watch out: Forgetting the angle/360 and working out the whole circle.
Volume of a cylinder
- Volume of a prism = area of the cross-section × length.
- For a cylinder: πr² × h.
- Give units cubed.
Watch out: Using the diameter instead of the radius.
Surface area
- A cuboid has 6 faces in 3 matching pairs.
- Find the area of one of each pair.
- Add the three areas and double it.
Watch out: Working out the volume. Surface area is the area of all the faces.
Volume of a prism
- Find the area of the cross-section (the end face).
- Volume = cross-section area × length.
- cm³ to litres: divide by 1000.
Watch out: Leaving the answer in cm³ when the question asks for litres.
Arc length
- The arc is a fraction of the circumference: angle/360 × πd.
- For the perimeter of a sector, add the two radii.
- Round at the end.
Watch out: Using πr², which gives an area, not a length.
Cones and spheres
- Use the formula given on the paper.
- Substitute carefully, using the radius.
- Use your calculator in one go and round at the end.
Watch out: Mixing up slant height and perpendicular height.
Working backwards
- Write the formula with the numbers in: π × r² × h = volume.
- Divide by π and by h to get r².
- Square root to get r.
Watch out: Forgetting the square root at the end.
Area of a segment
- Find the area of the sector: angle/360 × πr².
- Find the area of the triangle: ½ × r × r × sin(angle).
- Segment = sector − triangle.
Watch out: Forgetting to take the triangle away.
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