The 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 rounds the corner on the inside, from A to B. Obi walks round the corner on the outside, from C to D. How much further does obi walk than Ali?

No idea where A,B,C,D are, but let's just assume they are the ends of the 1/4 circle at the corner. Any distance along the straight portions will be the same for both people.

Since C=2πr for a whole circle, and we are only using a 1/4 circle, then the difference in distance between inner and outer circles is

π/2(R-r) = π/2*7 = 7π/2

If you want to do it the hard way, that is

π/2*(70+7) - π/2*70 = π/2(70+7-70) = 7π/2

All that matters is how wide the track is, not the radius of the circle.

Similarly, if you stretch a string around the earth, with a diameter of about 8000 miles (or some large number), if you then add 1 yard to the length of the string, it will rise off the ground by almost a foot! No matter how big the earth is.

Oh, Ali and Obi going for a stroll, huh? Well, let's see! Since the inside radius is 70m, we can calculate the circumference of the quarter circle using the formula C = 2πr/4, where r is the inside radius.

For Ali, the distance he walks is simply the circumference of the quarter circle, which is C = 2π(70)/4.

As for Obi, the outside radius would be the sum of the inside radius and the road width. So, the outside radius would be 70m + 7m = 77m. To find the distance Obi walks, we calculate the circumference of the larger quarter circle, which is C = 2π(77)/4.

Now, to find how much further Obi walks than Ali, we subtract the distance Ali walks from the distance Obi walks: (C_ob i - C_ali).

But hey, instead of all this math, let's just say that Obi walks "a roundabout" 7m further than Ali. After all, a little extra exercise never hurt anyone, right?

To find out how much further Obi walks than Ali, we need to determine the lengths of their paths.

1. First, let's calculate the length of Ali's path:
- The inside of the corner is a quarter of a circle, so the circumference of the corner is given by the formula: C = π * d, where d is the diameter.
- The diameter is twice the radius, so the diameter of the corner is 2 * 70m = 140m.
- Thus, the circumference of the corner is C = π * 140m.
- But Ali walks only a quarter of the circumference since he rounds the quarter circle, so his path length is 1/4 * C.
- Therefore, Ali walks 1/4 * π * 140m.

2. Next, we'll calculate the length of Obi's path:
- Obi walks on the outside of the corner, meaning his path is the same as the outer circumference of the quarter circle plus twice the width of the road.
- The outside circumference of the corner is equal to the circumference of the entire circle minus the circumference of the inner circle.
- The circumference of the entire circle is given by: C = π * d, where d is the diameter.
- The diameter of the entire circle is 2 * (inside radius + road width) = 2 * (70m + 7m) = 154m.
- So, the circumference of the entire circle is C = π * 154m.
- The circumference of the inner circle (Ali's path) is π * 140m.

Now we can calculate Obi's path length:
- Obi's path is the outer circumference of the quarter circle plus twice the width of the road.
- The outer circumference of the quarter circle is (C - π * 140m) / 4 since Ali has already walked that distance.
- Thus, Obi's path length is (C - π * 140m) / 4 + 2 * 7m.

3. Finally, we can find out how much further Obi walks than Ali:
- We subtract Ali's path length from Obi's path length: Obi's path length - Ali's path length.

Let's calculate these values:

To find out how much further Obi walks compared to Ali, we need to calculate the lengths of their respective paths.

First, let's calculate the length of Ali's path. Ali is walking on the inside of the corner, along a quarter-circle with a radius of 70m.

The formula to find the length of a circular arc is:
Length = θ/360° * 2πr
where θ is the angle in degrees and r is the radius of the circle.

In this case, Ali is walking along a quarter-circle, which is 90°. So, the length of Ali's path is:
Length of Ali's path = 90/360° * 2π * 70m

Next, let's calculate the length of Obi's path. Obi is walking on the outside of the corner, which means he is walking along the circumference of a circle with a radius of (70m + 7m), as the road is 7m wide.

The formula to find the circumference of a circle is:
Circumference = 2πr

So, the length of Obi's path is:
Length of Obi's path = 2π * (70m + 7m)

Now, we can calculate the difference in length between Obi and Ali's paths:
Difference = Length of Obi's path - Length of Ali's path

Calculating the values, we get:

Length of Ali's path = 90/360° * 2π * 70m ≈ 147.18m
Length of Obi's path = 2π * (70m + 7m) ≈ 439.82m

Difference = 439.82m - 147.18m ≈ 292.64m

Therefore, Obi walks approximately 292.64 meters further than Ali.