Page 242 - ICSE Math 7

Solution: Circumference of the circular sheet = 132 cm

22
∴ 2 × 7 × r = 132 cm (Circumference = 2pr)
132 × 7
⇒ r = cm = 21 cm
2 × 22
2
Area of the circular sheet = pr = 22 × 21 cm × 21 cm
7
= 1,386 cm 2

Example 14: A gardener wants to fence a circular garden of diameter 21 m. Find the length of the
rope he needs to purchase, if he fences the circumference twice. Also find the total cost
22
of the rope at the rate of ` 5 per metre. (Take p = 7 )

Diameter 21
Solution: Radius of the garden = = m
2 2
22 21 462
Circumference of the garden = 2pr = 2 × × = = 66 m
7 2 7
Rope needed to make 2 rounds of fence = 66 m × 2 = 132 m
Rate at which the rope is available = ` 5 per metre
∴ total cost of the required rope = ` 5 × 132 = ` 660

Example 15: Find the perimeter of the given figure enclosed by a semicircle
and a diameter.
22
Solution: Circumference of the circle = 2pr = 2 × 7 × 7 cm, = 44 cm
1 7 cm
Perimeter of the figure = (Circumference of circle) + Diameter
2
1
= × 44 cm + 2 × 7 cm = 22 cm + 14 cm = 36 cm
2
Example 16: Shazli took a wire of length 44 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 p = )
7
Solution: Since wire of length 44 cm is bent into a circle
∴ circumference of circle = 44 cm
22
∴ 2 × × r = 44 (Circumference of circle = 2pr)
7
44 × 7
∴ r = = 7 cm
44
22
2
Area of the circle = pr = × 7 cm × 7 cm = 154 cm 2
7
Let the same wire is bent into a square of side s,
Perimeter of the square = 44 cm
4 × s = 44 cm (Perimeter of square = 4 × s)
44
∴ s = cm = 11 cm
4

228