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\ 28-Jan-2025 Surender Prajapati Proof-5 Reader’s Sign _______________________ Date __________

Example 24: From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area
of the remaining sheet. (Take p = 3.14)
Solution: Area of circular sheet (with R = 4 cm)
2
2
= pR = p × 4 × 4 cm = 16 p cm 2
Area of circular sheet removed (with r = 3 cm) 3 cm
2
2
= pr = p × 3 × 3 cm = 9 p cm 2 O r
2
\ Area of the remaining sheet = (16 p – 9 p) cm = 7 p cm 2 4 cm R
2
= (7 × 3.14) cm = 21.98 cm 2
Thus, the area of remaining sheet is 21.98 cm 2
Example 25: Roopam took a wire of length 88 cm and bent it into the shape of a circle. Find
the radius of that circle. Also, find its area. If the same wire is bent into the shape of a square,
what will be the length of each of its sides? Which figure encloses more area, the circle or
 22 
the square? Take π= 7  .



Solution: Length of the wire = Circumference of circle Think and Answer
88 cm = 2pr
A horse is tied with a rope in
22 the middle of a square-shaped
88 cm = 2 × × r
7 field of side 26 m. The length of
88 7 the rope is half the size of each
×
r = cm = 14 cm
×
222 side of the field. How much
Area of circle = pr 2 area of the field the horse
cannot graze?
 22 
×
2
=   7 × 14 14 cm = 616 cm 2

Now, rebent the wire into a square shape.
\ Perimeter of the square = circumference of the circle
4 × a = 88 cm [where ‘a’ is the side of square]

a = 88 cm = 22 cm
4
2
2
\ Area of the square = (side) = (22 cm) = 484 cm 2
Since, area of the circle > area of the square
\Circle will enclose more area.

Practice Time 13C

1. Complete the table:

Radius (r) of circle Diameter (d) of circle Circumference of circle Area of circle
(a) 4 cm

(b) 14 cm
(c) 144 cm

(d) 616 sq. m

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