AP State Syllabus AP Board 7th Class Maths Solutions Chapter 13 Area and Perimeter Ex 5 Textbook Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 13th Lesson Area and Perimeter Exercise 5

Question 1

Find the circumference of a circle whose radius is

(i) 35cm (ii) 4.2cm (iii) 15.4 cm

Solution:

i) Given: r= 35 cm

Circumference of the circle = 2πr = 2 × \(\frac{22}{7}\) × 35 = 220 cms.

ii) Given : r = 4.2 cm

Circumference of the circle = 2πr = 2 × \(\frac{22}{7}\) × 4.2 26.4 cms

iii) Given: r = 15.4cm

Circumference of the circle = 2πr = 2 × \(\frac{22}{7}\) × 15.4 = 96.8 cms

Question 2.

Find the circumference of circle whose diameter is

(i) 17.5 cm (ii) 5.6 cm (iii) 4.9 cm

Note : take π = \(\frac{22}{7}\) in the above two questions.

Solution:

i) Given : d = 17.5 cm

Circumference of the circle = πd = \(\frac{22}{7}\) × 17.5 = 55 cm

ii) Given d = 5.6 cm

Circumference of the circle = πd = \(\frac{22}{7}\) × 5.6 = 17.6 cm

iii) Given d = 4.9 cm

Circumstances of the circle = πd = \(\frac{22}{7}\) × 4.9 = 15.4 cm

Question 3.

(i) Taking π = 3.14, find the circumference of a circle whose radius is

(a) 8 cm (b) 15 cm (c) 20cm

(ii) Calculate the radius of a circle whose circumference is 44cm?

Solution:

i) a) Given r = 8 cm π = 3.14

Circumference of circle = 2πr

= 2 × 3.14 × 8 = 50.24cm

b) Given r = 15cm

Circumference of circle = 2πr

= 2 × 3.14 × 15 = 942cm

c) Given r 20cm

Circumference of circle = 2πr

= 2 × 3.14 × 20 = 125.6cm

ii) Given,

Circumference = 44cm

Circumference of a circle = 2πr

2 × \(\frac{22}{7}\) x r =

2 × 22 × r = 44 x 7

r = \(\frac{44 \times 7}{2 \times 22}\) = 7cm

∴ radius of the circle = 7cm.

Question 4.

If the circumference of a circle is 264 cm, find its radius. Take π = \(\frac{22}{7}\)

Solution:

Given : Circumference = 264 cm

Circumference of a circle = 2πr = 2 × \(\frac{22}{7}\) x r = 264

2 × 22 × r = 264 × 7

r = \(\frac{264 \times 7}{2 \times 22}\) = 42

∴ radius of the circle = 42 cm.

Question 5.

If the circumference of a circle is 33 cm, fmd its diameter.m

Solution:

Given circumference = 33cm

Circumference of a circle = πd

\(\frac{22}{7}\) × d = 33

22d = 33 × 7

d = \(\frac{33 \times 7}{22}=\frac{21}{2}\) = 10.5cm

∴ diameter of the circle = 10.5 cm

Question 6.

How many times will a wheel of radius 35cm be rotated to travel 660 m?

(Take π = \(\frac{22}{7}\)).

Solution:

Given radius = 35cm.

Circumference of the circle = 2πr

= 2 × \(\frac{22}{7}\) × 35

= 220cm.

∴ The number of times the wheel will he rotated = \(\frac{660}{220}\) = 3 times.

Question 7.

The ratio of the diameters of two circles is 3 :4. Find the ratio of their circumferences.

Solution:

Given: Ratio of diameter = d_{1} : d_{2} = 3 : 4

Ratio of their circumferences C_{1} : C_{2} = πd_{1} : πd_{1}

= \(\frac{22}{7}\) × 3: \(\frac{22}{7}\) : 4 = 3 : 4

Question 8.

A road roller makes 200 rotations in covering 2200 m.

Find the radius of the roller.

Solution:

Given : Road roller makes 200 rotations covering a distance = 2200m

(i.e.,) 200 × circumference = 2200

200 × 2 × π × r = 2200

200 × 2 \(\frac{22}{7}\) × r = 2200

r = 2200 × \(\frac{7}{22} \times \frac{1}{200} \times \frac{1}{2}=\frac{7}{4}\) = 1.75m

Question 9.

The minute hand of a circular clock is 15 cm.

How far does the tip of the minute hand move in 1 hour?

(Take π = 3.14)

Solution:

Given : The length of minute hand = 15cm

In one hour it completes a rotation.

i.e. distance covered by its tip = circumference of the circle with a radius 15cm

22 660

= 2 × \(\frac{22}{7}\) × 15 = \(\frac{660}{7}\) cm = 94.28cm

Question 10.

A wire is bent in the form of a circle with radius 25 cm. It is straightened and made ¡rito a square. What is the length of the side of the square?

Solution:

Given: Radius of the circle 25 cm .

Circumference of the circle = Perimeter of the square

2πr = 4 × side

4 × side=2 × \(\frac{22}{7}\) × 25

Side = 2 × \(\frac{22}{7}\) × 25 × \(\frac{1}{4}\) = \(\frac{275}{7}\) = 39.28

∴ Side of square = 39.28 cm