Video: Pack 1 β€’ Paper 2 β€’ Question 3

Pack 1 β€’ Paper 2 β€’ Question 3

03:04

Video Transcript

Ryan walks around a semicircular enclosure with diameter 20 metres. Six cones A, B, C, D, E, and F are placed at equal intervals around the curved edge of the semicircle as shown. Ryan walks from cone A to cone F along the curved edge of the semicircular enclosure. Work out the distance that Ryan walks between cones C and D. Give your answer to one decimal place.

Here, we are looking to find the length of a part of the circumference of the circle. We know that the formula for circumference of a circle is πœ‹ times diameter or two πœ‹π‘Ÿ. We are given that the diameter of the semicircle is 20 metres. Therefore, the formula πœ‹ times diameter is much more useful than two πœ‹π‘Ÿ. Since the diameter is 20 metres, the circumference of the whole circle is πœ‹ times 20 or 20πœ‹.

At this stage, we won’t type this into our calculator. Instead, we’ll leave our answer in terms of πœ‹ until the very end. This will prevent us from making any mistakes from rounding too early. Our shape is a semicircle β€” that’s half a circle. So we can find the total length that Ryan walks by dividing this by two. 20πœ‹ divided by two is 10πœ‹.

The question wants us to calculate the distance that Ryan walks between the cones C and D. Notice how each cone is in equal distance apart, creating five equal gaps between each cone. We can divide 10πœ‹ by five then to work out the gap between each cone. 10πœ‹ divided by five is two πœ‹. Two multiplied by πœ‹ is 6.2831. We are told to give our answer correct to one decimal place. Therefore, the distance that Ryan walks between cones C and D is 6.3 metres.

Cones B, C, D, and E are then randomly placed along the curved edge of the semicircle. And A and F are left in their original position. If Ryan walks from cone A to cone F along the curved edge of the semicircle now, has the mean distance that Ryan walks between one cone and the next changed? You must explain your answer.

Let’s first recall the definition of the mean average. Another way of saying this is the mean distance that Ryan travels is given by the total distance travelled divided by five. Now, regardless of where the cones are placed around the semicircular enclosure, the total distance that he travels remains unchanged. The number of gaps also remains unchanged. There are still five gaps that he needs to walk between. This means then that no, the total distance and the number of gaps remain the same. So the mean distance does not change.

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