### 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 times diameter or two ππ. We are given that the diameter of
the semicircle is 20 metres. Therefore, the formula π times
diameter is much more useful than two ππ. Since the diameter is 20 metres,
the circumference of the whole circle is π times 20 or 20π.

At this stage, we wonβt type this
into our calculator. Instead, weβll leave our answer in
terms of π until the very end. This will prevent us from making
any mistakes from rounding too early. Our shape is a semicircle β thatβs
half a circle. So we can find the total length
that Ryan walks by dividing this by two. 20π divided by two is 10π.

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 by five then to
work out the gap between each cone. 10π divided by five is two π. Two multiplied by π 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.

Letβs 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.