Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 3 • Question 8

Use the height of the man to estimate the height of the windmill. Include the height of the sail in your estimate.

02:52

Video Transcript

Use the height of the man to estimate the height of the windmill. Include the height of the sail in your estimate. This drawing has been drawn to scale.

Now, in math world, the word “estimate” doesn’t mean just look at the drawing and have a guess of the number that looks about right to you; you got to justify your estimate with some sort of a calculation. So in this case, we got to take some measurements from the drawing and we got to calculate the approximate height of the windmill using those measurements.

So we’re gonna need to use a ruler as accurately as we can to measure these distances on the drawing — these heights — and then perform some calculations using those measurements. Before we do any measuring though, it is worth mentioning that you need to print this out at 100 percent scale on your printer. If you use any other figure and do scale to fit or something like that, then you’ll end up with different measurements and a different answer at the end of this question.

So we’ve carefully lined up the zero point of the ruler with the top of the man’s head. And looking down at that scale, we can see that the height of the man on the drawing is twelve millimetres or 1.2 centimetres. And, similarly, lining up the zero on our ruler with the top of the sail, if we measure down, we can see that the height of the windmill above the ground is 14 centimetres on this drawing.

And from this, we can see that 1.2 centimetres on the drawing represents 1.8 metres in real life. And we can represent this as a ratio: 1.2 centimetres on the drawing represents 1.8 metres in real life. Now, I can divide 1.2 by 1.2 itself to get one centimetre. And using this technique, I can find out what one centimetre on the drawing represents in real life. And 1.8 divided by 1.2 gives us 1.5. So one centimetre on the drawing represents 1.5 metres in real life.

But our windmill was 14 centimetres on the drawing. So it’s gonna be 14 times bigger than 1.5 metres in real life. And 1.5 times 14 is 21. So 14 centimetres on the drawing — the height of a windmill in the drawing — represents 21 metres in real life. So the answer is the estimated height of the windmill is 21 metres.

Now when you take measurements in question, you’re allowed a little bit of leeway. So we got 1.2 centimetres and 14 centimetres. And if your measurements are within one or two millimetres of that and you follow the right method through to the end of the question even if you got a different answer to ours, but it matches the numbers that you measured, then you’re still get full mark potentially for this question.

So clearly show the measurement that you took, clearly show the scale factor that you used — so one centimetres on the drawing represents 1.5 metres in real life — and then clearly show your answer.

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