PROBLEMS ON FINDING AREA OF CIRCLE

Find the area of :

Problem 1 :

Solution :

Area of a circle = πr²

= 3.14 × (7)²

= 3.14 × 49

= 153.86

So, the area is 153.86 cm².

Problem 2 :

Solution :

r = d/2

= 18/2

= 9

Area of a circle = πr²

= 3.14 × (9)²

= 3.14 × 81

= 254.34

So, the area is 254.34 cm².

Problem 3 :

Solution :

r = d/2

= 10.2/2

= 5.1

Area of a semicircle = πr²/2

= (3.14 × (5.1)²)/2

= 40.85

So, the area is 40.85 cm²

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 = πr²

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 m²

b) The visible area = l × w

= 5.2 × 3.5

= 18.2

So, the visible area is 18.2 m²

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 = πr²

= 22/7 × (0.8)²

= 3.14 × 0.64

= 2

Area of a circular table is 2 m².

A rectangular tablecloth = 2 × 2

= 4

Area of rectangular cloth is 4 m².

So, area of the tablecloth overlaps the table = 4 – 2

= 2 m²

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(πr²/4) ==> πr²

r = D/2

= 40/2

r = 20

= π × (20)²

= 400π m

= 400(3.14)

Approximately 1257 m²

c) Area of the garden a = a²

= 40 × 40

= 1600 m

d) Area of the flower bed = area of garden - area of lawn

= 1600 - 1257

= 343 m²

So, area of the flower bed is 343 m²

e) Length of edge

= 4(Perimeter of quarter (circle curve only))

= 4 (2πr/4)

= 2πr

= 2 (3.14) (20)

= 125.6

Approximately 126 m.