Question

A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)

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Solution

The correct option is **B**

22857.14 m^{2}

We need to find the unallocated area within the stadium.

The unallocated area should be = The total circular area of the stadium – Area of the hockey court - Area of the Javelin Range.

The area of circular stadium =π×r2

= π×2002

= 40000π

The area of hockey court (square), we know that the radius of the stadium forms the diagonal of the hockey court.

Therefore the sides of the hockey court will be **a =r√2**, (applying **Pythagoras Theorem **in a square)

Then, the area of the square =a2

=(r√2)2

=r22

= 20022

= **20000 m2**

Javelin Range is a right angled triangle

area of the right triangle = 12×r×r

= 12×200×200

= **20000m2**

Therefore the unallocated area in the stadium =Total area of stadium – Area of the hockey court – Area of the Javelin Range

=40000π−20000−20000

=40000(π−1) m2

The unallocated area within the stadium is **40000(π−1) m2****.**

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