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 = d1 : d2 = 3 : 4
Ratio of their circumferences C1 : C2 = πd1 : πd1
= $$\frac{22}{7}$$ × 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