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Find the circumference of the circles with the following radius: (Takeπ
)
(a) 14 cm (b) 28 mm (c) 21 cm
(a) r = 14 cm
Circumference = 2πr 
= 88 cm
(b) r = 28 mm
Circumference = 2πr 
= 176 mm
(c) r = 21 cm
Circumference = 2πr 
= 132 cm
Find the area of the following circles, given that:
(a) radius = 14 mm (Takeπ
) (b) diameter = 49 m
(c) radius = 5 cm
(a) r = 14 mm
Area = πr2
= 616 mm2
(b) d = 49 m
r =
Area = πr2 =
= 1886.5 m2
(c) r = 5 cm
Area = πr2 =
= 78.57 cm2
If the circumference of a circular sheet is 154m, find its radius. Also find the area of
the sheet. (Takeπ)
Circumference = 2πr =154 m
Area = πr2 = 
= 
= 1886.5 m2
A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the costs of the rope, if it cost Rs 4 per meter. (Takeπ
)
d = 21 m
r =
Circumference = 2πr =
= 66 m
Length of rope required for fencing = 2 × 66 m = 132 m
Cost of 1 m rope = Rs 4
Cost of 132 m rope = 4 × 132 = Rs 528
From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Takeπ = 3.14)
Outer radius of circular sheet = 4 cm
Inner radius of circular sheet = 3 cm
Remaining area = 3.14 × 4 × 4 − 3.14 × 3 × 3
= 50.24 − 28.26
= 21.98 cm2
Saima 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 meter of the lace costs Rs 15.( Takeπ = 3.14)
Circumference = 2πr
Cost of 1 m lace = Rs 15
Cost of 4.71 m lace = 4.71 × 15 = Rs 70.65
Find the perimeter of the adjoining figure, which is a semicircle including its diameter.
Radius = 5 cm
Length of curved part = πr
= 15.71 cm
Total perimeter = Length of curved part + Length of diameter
= 15.71 + 10 = 25.71 cm
Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is Rs 15/m2. (Take π = 3.14)
Diameter = 1.6 m
Radius 
= 0.8 m
Area = 3.14 × 0.8 × 0.8
= 2.0096 m2
Cost for polishing 1 m2 area = Rs 15
Cost for polishing 2.0096 m2 area = 15 × 2.0096 = 30.14
Therefore, it will cost Rs 30.14 for polishing such circular table.
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 the square? (Takeπ
)
Circumference = 2πr = 44 cm
r = 7 cm
Area = πr2
If the wire is bent into a square, then the length of each side would be =
Area of square = (11)2 = 121 cm2
Therefore, circle encloses more area.
From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in the following figure). Find the area of the remaining sheet. (Takeπ
)
Area of bigger circle =
= 616 cm2
Area of 2 small circles = 2 × πr2
= 77 cm2
Area of rectangle = Length × Breadth = 3 × 1 = 3 cm2
Remaining area of sheet = 616 − 77 − 3 = 536 cm2
A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? (Take π = 3.14)
Area of square-shaped sheet = (Side)2 = (6)2 = 36 cm2
Area of circle = 3.14 × 2 × 2 = 12.56 cm2
Remaining area of sheet = 36 − 12.56 = 23.44 cm2
The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take π = 3.14)
Circumference = 2πr = 31.4 cm
2 × 3.14 × r = 31.4
r = 5 cm
Area = 3.14 × 5 × 5 = 78.50 cm2
A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (π = 3.14)
Radius of flower bed 
= 33 m
Radius of flower bed and path together = 33 + 4 = 37 m
Area of flower bed and path together = 3.14 × 37 × 37 = 4298.66 m2
Area of flower bed = 3.14 × 33 × 33 = 3419.46 m2
Area of path = Area of flower bed and path together − Area of flower bed
= 4298.66 − 3419.46 = 879.20 m2
A circular flower garden has an area of 314 m2. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take π = 3.14)
Area = πr2 = 314 m2
3.14 × r2 = 314
r2 = 100
r = 10 m
Yes, the sprinkler will water the whole garden.
Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)
Radius of outer circle = 19 m
Circumference = 2πr = 2 × 3.14 × 19 = 119.32 m
Radius of inner circle = 19 − 10 = 9 m
Circumference = 2πr = 2 × 3.14 × 9 = 56.52 m
How many times a wheel of radius 28 cm must rotate to go 352 m?
(Take π 
)
r = 28 cm
Circumference = 2πr =
= 176 cm
Number of rotations =
Therefore, it will rotate 200 times.
The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take π = 3.14)
Distance travelled by the tip of minute hand = Circumference of the clock
= 2πr = 2 × 3.14 × 15
= 94.2 cm
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