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.)

A

22853.14 m2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

22857.14 m2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

20000 m2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

62857.14 m2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B 22857.14 m2 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.

Suggest Corrections
0
Related Videos
Visualisations
MATHEMATICS
Watch in App