Measurement

How much paint covers a water tank? How many litres does a swimming pool hold? How close is "close enough" when you measure? In this topic you'll revise the area of flat shapes, then move into three dimensions: unfolding prisms into nets, finding how much material covers a solid (its surface area) and how much space is inside it (its volume), first for prisms and then for cylinders. Along the way you'll learn why every measurement is really an estimate, and how to work out the size of the error.

What you'll learn

• 9.01 Area: the area formulas for rectangles, triangles, parallelograms, trapeziums, kites and circles, converting units of area, and working backwards from an area.
• 9.02 Area of composite shapes: adding and subtracting simple shapes, including semicircles, quadrants and other sectors.
• 9.03 Nets of prisms: faces, edges and vertices, which nets fold into which prisms, and drawing nets with the right measurements.
• 9.04 Surface area of prisms: adding up the faces of rectangular, triangular, trapezoidal and other prisms, using SA = 2A + Pl.
• 9.05 Volume of prisms: V = Ah, units of volume and capacity, and real problems with pools, concrete and rainfall.
• 9.06 Accuracy of measurement: limits of accuracy, absolute, relative and percentage error, and very large and very small measurements in scientific notation.
• Investigation: volume versus area. Find the biggest box you can fold from one sheet of card, and discover why small animals lose heat faster than big ones.
• 9.07 Surface area of cylinders: the net of a cylinder, SA = $2\pi r^2 + 2\pi rh$, and open cylinders, half cylinders and pipes.
• 9.08 Volume of cylinders: V = $\pi r^2 h$, capacity in litres, and finding a missing radius or height.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: simpler shapes and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: composite solids, working backwards and multi-step problems, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.