Perimeter of first semi-circle =π×r=722​×21​=711​

Perimeter of second semi-circle =722​×1=722​

So, d=722​−711​=711​

S13​=213​(2×711​+711​×12)

=213​(722+132​)=213​×7154​=143 cm

**Introduction:**
In this problem, we are given a spiral made up of seven successive semicircles with centers alternatively at points A and B. The radii of the semicircles are given as 0.5 cm, 1 cm, 1.5 cm, and so on. We need to find the total length of the spiral.

**Approach:**
To find the total length of the spiral, we need to find the length of each semicircle and then add them up.

**Calculating the Length of a Semicircle:**
The length of a semicircle is given by the formula L = πr, where L is the length and r is the radius.

**Calculating the Length of Each Semicircle:**
We are given the radii of the semicircles as 0.5 cm, 1 cm, 1.5 cm, and so on. We can use these radii to calculate the length of each semicircle.

- Length of the first semicircle with a radius of 0.5 cm:
L1 = π * 0.5 = 1.57 cm (approx.)

- Length of the second semicircle with a radius of 1 cm:
L2 = π * 1 = 3.14 cm (approx.)

- Length of the third semicircle with a radius of 1.5 cm:
L3 = π * 1.5 = 4.71 cm (approx.)

**Finding the Total Length of the Spiral:**
To find the total length of the spiral, we need to add up the lengths of all the semicircles. As there are a total of seven semicircles, we can calculate the total length as follows:

Total length = L1 + L2 + L3 + ... + L7

**Calculating the Total Length of the Spiral:**
Using the lengths of the semicircles calculated above, we can find the total length of the spiral.

Total length = 1.57 + 3.14 + 4.71 + ... + L7

Substituting the values of the lengths of the semicircles, we can calculate the total length of the spiral.

**Note:** As the problem does not provide the length of the seventh semicircle, we cannot calculate the exact total length without that information. However, we can apply the above approach to find the approximate total length of the spiral using the given lengths of the first six semicircles.