Question

In the figure, there is a jogging track that has to be renovated. The cost of renovation is Rs. 15 per square meters. For the circular parts, the inner and outer radii are 6 m and 8 m respectively. If the total cost of renovation is Rs. 2,520, find the length of AB.

• A. 10 m
• B. 15 m
• C. 20 m
• D. 25 m

Answer 1

The correct option is C

20 m

There are two semi-circular parts (green parts) which add up to be a complete circle.

So, area of the circular part of the track =$\pi \left[\right(outerradius{)}^2-\left(innerradius{)}^2\right]$

$=\pi (8^2-6^2)=\left(\frac{22}{7}\right)\times 14\times 2=88m^2$ (Using identity $a^2–b^2$ = (a + b)(a - b))

Now, with the inner and outer radius, we can say that width of the track is 2 m. Let us assume AB, i.e. length of the parallelograms as x.

So, areas of two parallelograms = 2 $\times$ x $\times$ 2 = 4x

Total area = (4x + 88) $m^2$

To renovate this, cost is Rs. 2,520.

(4x + 88) $\times$ 15 = 2520

4x + 88 = 168

4x = 80

x = 20

So, AB = 20 m