Circle

Exercise 11.3 Part 3

Question 11: 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)

Solution: Given Side of square sheet of aluminium sheet = 6 cm
Radius of circle which is cut out from aluminium sheet = 2 cm

Procedure: Calculate the area of square sheet.
Calculate the area of circle.
To calculate the area of left over aluminium sheet Subtract the area of circle from area of square sheet.

Area of square sheet = side `xx` side = 6xx6= 36` cm2

Area of circle `= π r^2`
`= 3.14 xx 2xx2= 12.56` cm2

Area of left over aluminium sheet = Area of square sheet — Area of circle
`= 36—12.56= 23.44` cm2


Question 12: The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take π = 3.14)

Solution: Given, Circumference of circle = 31.4 cm

Circumference `= 2 π r`
Or, `31.4= 2 xx 3.14 xx \r`
Or, `r = (31.4)/(2xx3.14) = 5` cm

Area of circle `= π r^2`
`= 3.14 xx5^2= 3.14 xx 25 = 78.50` cm2

Question 13: A circular flower bed is surrounded by a path of 4 m wide. The diameter of the flower bed is 66m. What is the area of this path? (π = 3.14)

semi circle

Solution:Given; Diameter of the circular flower bed = 66m, Width of path around flower bed = 4 m

Therefore, diameter of bigger circle = 66 m + 4 m + 4 m = 74m
Radius of flower bed = 33 cm
Radius of bigger circle = 37 cm

Area of bigger circle `= π r^2`
`= 3.14 xx 37 xx 37 = 4298.66` sq m

Area of smaller circle `= πr^2`
`= 3.14 xx 33 xx 33 = 3419.46` sq m

Area of path = Area of flower bed with path — Area of flower bed
`= 4298.66— 3419.46= 879.20` m2


Question 14: A circular flower garden has an area of 314 m2. A sprinkler at the center of the garden can cover an area that has a radius of 12m. Will the sprinkler water the entire garden? (Take π = 3.14)

Solution:Given; Area of circular flower garden = 314 m2
radius of area that can cover by sprinkler = 12m

Area that can cover by sprinkler `= π r^2`
`= 3.14 xx 12^2= 3.14 xx 144`
`= 452.16` m2

Because, Area of circular flower garden > the area that can cover by sprinkler
Therefore, sprinkler can water the entire garden.

Question 15: Find the circumference of the inner and the outer circles, shown in the adjoining figure?

semi circle

Solution: Radius of inner circle = Radius of whole circle — Width of outer circle without inner circle
= 19m — 10m = 9m

Circumference of inner circle `= 2 π r`
`= 2 xx 3.14 xx 9 = 6.28 xx 9 = 56.52` m

Circumference of outer circle `= 2 π r`
`= 2 xx 3.14 xx 19 = 119.32` m


Question 16: How many times a wheel of radius 28 cm must rotate to go 352m?

Solution: Given, Radius of wheel = 28cm, Distance to be covered = 352 m = 35200 cm.

Circumference `= 2 π r`
`= 2 xx(22)/(7)xx 28`
`= 2 xx22 xx4 = 176` cm

Number of rotations = Distance ÷ Circumference
`= 35200 ÷ 176 = 200`

Question 17: The minute hand of a circular clock is 15cm long. How far does the tip of the minute hand move in 1 hour. (Take π=3.14)

Solution: Length of minute hand = 15 cm = radius of circle

Process: To calculate the distance covered by minute hand, we have to calculate its circumference.

Circumference `=2πr = 2 xx 3.14 xx 15`
`= 6.28 xx15= 94.20` cm



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