What is Area of a Circle ?
Area of a Circle is the region covered or enclosed within its boundary. It is measured in square units.
The formula for area of a circle is
Area = πr²
(where r is the radius of a circle)
If the given diameter of a circle, then the radius is
Radius (r) = (Diameter)/2
Find the area of :
Problem 1 :
Solution :
Area of a circle = πr^{2}
= 3.14 × (7)^{2}
= 3.14 × 49
= 153.86
So, the area is 153.86 cm^{2}.
Problem 2 :
Solution :
r = d/2
= 18/2
= 9
Area of a circle = πr^{2}
= 3.14 × (9)^{2}
= 3.14 × 81
= 254.34
So, the area is 254.34 cm^{2}.
Problem 3 :
Solution :
r = d/2
= 10.2/2
= 5.1
Area of a semicircle = πr^{2}/2
= (3.14 × (5.1)^{2})/2
= 40.85
So, the area is 40.85 cm^{2}
Problem 4 :
A circular rug is laid on a tiled floor. Find :
a) the area of the rug
b) the visible area of the tiled floor.
Solution :
a) Area of the rug = πr^{2}
r = d/2
= 2.4/2
r = 1.2
= 3.14 × (1.2)^{2}
= 3.14 × 1.44
= 4.5216
So, area of the rug is 4.5216 m^{2}
b) The visible area = l × w
= 5.2 × 3.5
= 18.2
So, the visible area is 18.2 m^{2}
Problem 5 :
A circular table top has a diameter of 1.6 m. A rectangular tablecloth 2 m by 2 m is placed over the table top. What area of the tablecloth overlaps the table?
Solution :
Diameter of a circular table top = 1.6 m
A rectangular tablecloth = 2 m by 2 m
r = d/2
= 1.6/2
r = 0.8
area of a circular table = πr^{2}
= 22/7 × (0.8)^{2}
= 3.14 × 0.64
= 2
Area of a circular table is 2 m^{2}.
A rectangular tablecloth = 2 × 2
= 4
Area of rectangular cloth is 4 m^{2}.
So, area of the tablecloth overlaps the table = 4 – 2
= 2 m^{2}
Problem 6 :
The diagram shows plans for a garden which is 40 m by 40 m. it consists of 4 quarter circles of lawn with a flower bed in the middle as shown.
Find :
a) The perimeter of the garden
b) The total area of lawn
c) The total area of the garden
d) The area of the flower bed
e) The length of edging around the flower bed.
Solution :
a) The perimeter of the garden = 4 × 40
= 160 m
b) Area of lawn = 4 area of quarter circle
Area of lawn = 4(πr^{2}/4) ==> πr^{2}
r = D/2
= 40/2
r = 20
= π × (20)^{2}
= 400π m
= 400(3.14)
Approximately 1257 m^{2}
c) Area of the garden a = a^{2}
= 40 × 40
= 1600 m
d) Area of the flower bed = area of garden - area of lawn
= 1600 - 1257
= 343 m^{2}
So, area of the flower bed is 343 m^{2}
e) Length of edge
= 4(Perimeter of quarter (circle curve only))
= 4 (2πr/4)
= 2πr
= 2 (3.14) (20)
= 125.6
Approximately 126 m.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM