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Chapter 21 Mensuration II (Area of Circle) Exercise – 21.1

Question: 1

Find the circumference of a circle whose radius is

(i) 14 cm                      (ii) 10 m                      (iii) 4 km

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 1

Question: 2

Find the circumference of a circle whose diameter is

(i) 7 cm                        (ii) 4.2 cm                    (iii) 11.2 km

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 2

Question: 3

Find the radius of a circle whose circumference is

(i) 52.8 cm                   (ii) 42 cm                     (iii) 6.6 km

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 3

Question: 4

Find the diameter of a circle whose circumference is

(i) 12.56 cm                 (ii) 88 m                      (iii) 11.0 km

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 4

Question: 5

The ratio of the radii of two circles is 3 : 2. What is the ratio of their circumferences?

Solution:

We have, the ratio of the radii = 3 : 2

So, let the radii of the two circles be 3r and 2r respectively.

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 5

Question: 6

A wire in the form of a rectangle 18.7 cm long and 14.3 cm wide is reshaped and bent into the form of a circle. Find the radius of the circle so formed.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 6

Question: 7

A piece of wire is bent in the shape of an equilateral triangle of each side 6.6 cm. It is re-bent to form a circular ring. What is the diameter of the ring?

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 7

Question: 8

The diameter of a wheel of a car is 63 cm. Find the distance travelled by the car during the period, the wheel makes 1000 revolutions.

Solution:

It may be noted that in one revolution, the cycle covers a distance equal to the circumference of the wheel.

Now, the diameter of the wheel = 63 cm

∴ Circumference of the wheel = πd = 227 x 63 = 198 cm.

Thus, the cycle covers 198 cm in one revolution.

∴ The distance covered by the cycle in 1000 revolutions = (198 x 1000) = 198000 cm = 1980 m.

Question: 9

The diameter of a wheel of a car is 98 cm. How many revolutions will it make to travel 6160 metres.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 9

Question: 10

The moon is about 384400 km from the earth and its path around the earth is nearly circular. Find the circumference of the path described by the moon in lunar month.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 10

Question: 11

How long will John take to make a round of a circular field of radius 21 m cycling at the speed of 8 km/hr?

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 11

Question: 12

The hour and minute hands of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their tips in 2 days.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 12

Question: 13

A rhombus has the same perimeter as the circumference of a circle. If the side of the rhombus is 2.2 m. Find the radius of the circle.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 13

Question: 14

A wire is looped in the form of a circle of radius 28 cm. It is re-bent into a square form. Determine the length of the side of the square.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 14

Question: 15

A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 15

Question: 16

A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60 cm, calculate the speed per hour with which the boy is cycling.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 16

Question: 17

The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 km per hour?

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 17

Question: 18

A water sprinkler in a lawn sprays water as far as 7 m in all directions. Find the length of the outer edge of wet grass.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 18

Question: 19

A well of diameter 150 cm has a stone parapet around it. If the length of the outer edge of the parapet is 660 cm. then find the width of the parapet.

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 19

Question: 20

An ox in a kolhu (an oil processing apparatus) is tethered to a rope 3 m long. How much distance does it cover in 14 rounds?

Solution:

Chapter 21 Mensuration II (Area of Circle) Exercise 21.1 Question: 20

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