RD SHARMA SOLUTION CHAPTER –21 Mensuration – II | CLASS 7TH MATHEMATICS-EDUGROWN

Exercise 21.1

Question: 1

Find the circumference of a circle whose radius is

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

Solution:

Question: 2

Find the circumference of a circle whose diameter is

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

Solution:

Question: 3

Find the radius of a circle whose circumference is

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

Solution:

Question: 4

Find the diameter of a circle whose circumference is

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

Solution:

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.

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:

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:

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:

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:

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:

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:

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:

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:

Question: 15

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

Solution:

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:

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:

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:

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:

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:

Exercise 21.2

Question: 1

Find the area of a circle whose radius is

(i) 7 cm

(ii) 2.1 m

(iii) 7 km

Solution:

Question: 2

Find the area of a circle whose diameter is

(i) 8.4 cm

(ii) 5.6 m

(iii) 7 km

Solution:

Question: 3

The area of a circle is 154 cm2. Find the radius of the circle.

Solution:

Question: 4

Find the radius of a circle, if its area is

(i) 4 it cm²

(ii) 55.44 m²

(iii) 1.54 km²

Solution:

Question: 5

The circumference of a circle is 3.14 m, find its area.

Solution:

Question: 6

If the area of a circle is 50.24 m², find its circumference.

Solution:

Question: 7

A horse is tied to a pole with 28 m long string. Find the area where the horse can graze. (Take π = 22 / 7).

Solution:

Question: 8

A steel wire when bent in the form of a square encloses an area of 121 cm². If the same wire is bent in the form of a circle, find the area of the circle.

Solution:

Question: 9

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of of road.

Solution:

Question: 10

Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh(2r + h).

Solution:

Question: 11

The perimeter of a circle is 4πr cm. What is the area of the circle?

Solution:

Question: 12

A wire of 5024 m length is in the form of a square. It is cut and made a circle. Find the ratio of the area of the square to that of the circle.

Solution:

Question: 13

The radius of a circle is 14 cm. Find the radius of the circle whose area is double of the area of the circle.

Solution:

Question: 14

The radius of one circular field is 20 m and that of another is 48 m. find the radius of the third circular field whose area is equal to the sum of the areas of two fields.

Solution:

Question: 15

The radius of one circular field is 5 m and that of the other is 13 m. Find the radius of the circular field whose area is the difference of the areas of first and second field.

Solution:

Question: 16

Two circles are drawn inside a big circle with diameters 2/3rd and 1/3rd of the diameter of the  big circle as shown in Figure. Find the area of the shaded portion, if the length of the diameter of the circle is 18 cm.

Solution:

Question: 17

In Figure, the radius of quarter circular plot taken is 2 m and radius of the flower bed is 2 m. Find the area of the remaining field.

Solution:

Question: 18

Four equal circles, each of radius 5 cm, touch each other as shown in Figure. Find the area included between them. (Take π = 3.14).

Solution:

Question: 19

The area of circle is 100 times the area of another circle. What is the ratio of their circumferences?

Solution: