Page 246 - Start Up Mathematics_7

Example 20: Tanvi wants to put a lace on the edge of a circular table cover of diameter 1.5 m.
Find the length of the lace required and also find its cost if one metre of the lace costs
` 18. (Take π = 3.14)

Solution: Radius of the circular table cover = Diameter = 1.5 = 0.75 m
2
2
Circumference of the table cover = 2πr = 2 × 3.14 × 0.75 = 4.71 m
Cost of 1 m lace = ` 18
Cost of the lace required = ` 18 × 4.71 = ` 84.78

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

Example 22: Find the cost of polishing a circular table-top of diameter 3 m, if the rate of polishing
2
is ` 25 per m . (Take π = 3.14)
3
Solution: Radius of the circular table-top = Diameter = = 1.5 m
2
2
2
Area of the circular table-top = πr = 3.14 × 1.5 × 1.5 = 7.065 m 2
Rate of polishing = ` 25 per m 2
∴ cost of polishing the table-top = 25 × 7.065 = ` 176.62 (approximately)

Example 23: Find the perimeter of the given figure enclosed by a semicircle
and a diameter.
Solution: Circumference of the circle = 2πr = 2 × 22 × 7 = 44 cm O
7
1
Perimeter of the figure = (Circumference of circle) + Diameter 7 cm
2
1
= × 44 + 2 × 7 = 22 + 14 = 36 cm
2
Example 24: 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
22
area, the circle or the square? (Take π = 7 ) (NCERT)
Solution: Since wire of length 44 cm is bent into a circle
∴ circumference of circle = 44 cm
22
∴ 2 × × r = 44 (Circumference of circle = 2πr)
7
∴ r = 44 × 7 = 7 cm
44

2
Area of the circle = πr = 22 × 7 × 7 = 154 cm 2
7
Let the same wire is bent into a square of side s,

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