Question

The Indian Hockey Federation organized a friendly hockey match between India and Pakistan on a circular ground. The incomes from the ticket of this match shall be donated to an orphanage. Grass is Laid on the ground in the shape of a rectangle (as shown in figure)

(i) Find the radius of the stadium.
(ii) Write the formula to find the area of rectangular portion.
(iii) Find the circumference of the circular ground.
(iv) Find the perimeter of rectangular portion.
(v) Find the area of the rectangular portion.

Answer 1

Answer:

(I)

There's a rectangle lying within the circle.

Observe the mentioned sides of the rectangle and the diameter of the circle, you get a Right Angled Triangle!

Now, right-angled triangles are very helpful, because concerning them there is the Pythagoras Theorem which says:

Hypotenuse² = Perpendicular² + Base²

=> H² = 8² + 6²

=> H² = 64 + 36

=> H² = 100

=> H = 10

The diameter made the Hypotenuse, hence, the diameter is 10 meters.

Radius is half of diameter = 10/ 2

= 5 m

(ii)

Area of the rectangular portion = Length × Breadth

[Since it's only asked for its formula]

(iii)

Circumference of the circle =2 π r

= 2π × 5

= 10 π

= 31.4 m

(iv)

The perimeter of the rectangle = 2(length + breadth)

= 2(6 + 8)

= 2 × 14

= 28 m

(v)

Area of rectangular portion

(solving the expression of ii part)

= (8 × 6) m²

= 48 m²