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Solution: Let the inner and outer radii of the track be r m and (r + 3.5) m, respectively.

Inner circumference = 220 m
So, 2pr = 220 m

22
2 × × r = 220 m
7
220 7 3.5 m
×
⇒ r = m = 35 m
222 r + 3.5
×
Therefore, the inner radius of the track = 35 m
O r
And the outer radius of the track = (35 + 3.5) m = 38.5 m
22
Thus, the circumference of the outer circle = 2 × × 38.5 m = 242 m
7
Q The rate of fencing the track = `60 per m
\ Total cost of fencing the outer circle of the track = `(242 × 60) = `14,520
Thus, the total cost of fencing the outer circle of the track is `14,520.

Think and Answer

A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in figure.

16cm

Does the perimeter change? If it does change, by how much does it increase or decrease?

Area of a Circle

Area of a circle is the region occupied by the circle in a two-dimensional plane.
Let us perform an activity.

activity
• Make a cutout of a circle of any radius r and shade one half of the circle.
• Fold the circle into eight equal parts and cut the parts along the folds.
• Now, arrange the separate 8 pieces of the circle as shown in the figure below.

r

1
(2pr)
2
• The figure thus formed, it is roughly a parallelogram whose base is the half of the circumference of a circle
and height is equal to the radius.

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