Area, perimeter and volume: watch it solved step by step

Circles, cylinders, cones, spheres, cuboids and more: exact answers in π and as decimals, with the right units. Level: KS3 / GCSE. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: circle of radius 7 cm

1. Understanding the problem. A circle: first write down the measurements you are given, then pick the formula for each quantity asked for.
2. Area: the formula. The formula for the area of a circle.
3. Area: substitute. Put the measurements in, in the same order as the formula.
4. Area: calculate. Leave π as it is for the exact answer, then use π ≈ 3.14159 for a decimal.
5. Circumference: the formula. The formula for the circumference of a circle.
6. Circumference: substitute. Put the measurements in, in the same order as the formula.
7. Circumference: calculate. Leave π as it is for the exact answer, then use π ≈ 3.14159 for a decimal.
8. Sense check. Does the size look right? Lengths use the plain unit, areas use the unit squared and volumes the unit cubed. A slip in the unit is the most common lost mark.

Answer: area = 49π ≈ 153.94 cm²; circumference = 14π ≈ 43.98 cm

Practise area, perimeter and volume with problems the Lab marks for you.