A road is 7m wide. The corner is in the shape of a quarter of a circle. The inside radius of the corner is 70m. Ali walks round the corner on the inside, from A to B. Obi walls round the corner on the outside, from C to D. How much further does Obi walk than Ali? Use the value 3.14 for pi
radii = 70 and 77
circumferences = 2 pi * 77 and 2 pi * 70
1/4 of the circumferences = .5 * 77 pi and .5 * 70 pi
difference = .7 * 7 * pi = 4.9 pi
I knew the answer was 2πr ÷ 4
Ur answer is 11 if your pii is 22/7
I want to see the caculation even though my answer is 11
To find out how much further Obi walks than Ali, we first need to calculate the distances they each walk.
Ali walks on the inside of the corner, following the shape of a quarter circle. We can calculate the length of this arc by using the formula:
Arc length = (angle/360) x 2πr
Since Ali is walking along a quarter of a circle, the angle is 90 degrees or π/2 radians. The radius is given as 70m. So, we can calculate Ali's arc length as follows:
Ali's arc length = (π/2/360) x 2π(70)
= 0.25π x 2π(70)
= 0.25 x 3.14 x 2 x 70
= 0.25 x 3.14 x 140
≈ 109.9m
So, Ali walks approximately 109.9 meters.
Obi walks on the outside of the corner. To calculate the distance Obi walks, we need to find the total circumference of the circle with a radius of 70m, and then subtract Ali's arc length from it.
The circumference of a circle is given by the formula:
Circumference = 2πr
Substituting the radius value, we can calculate the total circumference as follows:
Total circumference = 2π(70)
= 2 x 3.14 x 70
= 6.28 x 70
≈ 439.6m
Now, to find how much further Obi walks than Ali, we subtract Ali's arc length from the total circumference:
Difference = Total circumference - Ali's arc length
= 439.6 - 109.9
= 329.7m
Therefore, Obi walks approximately 329.7 meters further than Ali.