Measurement

Section 1SI units and conversions

SI units are standard measurement units such as metre, kilogram, second, and litre-related volume units. Convert before calculating if the units do not match. Watch out: area and volume conversions are not the same as length conversions because area is squared and volume is cubed.

Section 2Perimeter and circumference

Perimeter is the total distance around a flat shape. For a circle, the perimeter is called circumference. Use C = 2πr or C = πd, where r is radius and d is diameter.

Section 3Area

Area measures the surface covered by a 2D shape. Common formulas include rectangle area = length x width, triangle area = 1/2 x base x height, and circle area = πr^2. Here's the trick: area answers use square units, like cm^2 or m^2.

Section 4Sectors

A sector is a slice of a circle. Its area is a fraction of the whole circle: sector angle / 360 x πr^2. Its arc length is sector angle / 360 x 2πr. The angle must be measured at the centre of the circle.

Section 5Surface area

Surface area is the total area of the outside faces of a 3D solid. A cuboid has 6 rectangular faces, so add the areas of all faces or use 2lw + 2lh + 2wh. Easy to mix up: surface area uses square units, not cubic units.

Section 6Volume

Volume measures the space inside a solid. Cuboid volume = length x width x height, and cylinder volume = πr^2h. Volume answers use cubic units such as cm^3 or m^3, unless the question asks for litres or millilitres.

Section 7Time, distance, and speed

Speed = distance / time, distance = speed x time, and time = distance / speed. Convert time units carefully before calculating. For example, 30 minutes is 0.5 hours, not 30 hours.