Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RD Sharma Solutions: Mensuration – I (Area of Circle Exercise 21.2)
Mensuration – I (Area of Circle Exercise 21.2) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download
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Page 1
1. Find the area of a circle whose radius is
(i) 7 cm
(ii) 2.1 m
(iii) 7 km
Solution:
(i) Given radius = 7 cm
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 cm
2
(ii) Given radius = 2.1 m
We know that area of circle = p r
2
A = (22/7) × (2.1)
2
A = 22/7 × 4.41
A = 13.86 m
2
(iii) Given radius = 7 km
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 km
2
2. Find the area of a circle whose diameter is
(i) 8.4 cm
(ii) 5.6 m
(iii) 7 km
Solution:
(i) Given diameter = 8.4 cm
Therefore radius, r = d/2 = 8.4/2 = 4.2
We know that area of circle = p r
2
A = (22/7) × (4.2)
2
Page 2
1. Find the area of a circle whose radius is
(i) 7 cm
(ii) 2.1 m
(iii) 7 km
Solution:
(i) Given radius = 7 cm
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 cm
2
(ii) Given radius = 2.1 m
We know that area of circle = p r
2
A = (22/7) × (2.1)
2
A = 22/7 × 4.41
A = 13.86 m
2
(iii) Given radius = 7 km
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 km
2
2. Find the area of a circle whose diameter is
(i) 8.4 cm
(ii) 5.6 m
(iii) 7 km
Solution:
(i) Given diameter = 8.4 cm
Therefore radius, r = d/2 = 8.4/2 = 4.2
We know that area of circle = p r
2
A = (22/7) × (4.2)
2
A = 55.44 cm
2
(ii) Given diameter = 5.6 cm
Therefore radius, r = d/2 = 5.6/2 = 2.8
We know that area of circle = p r
2
A = (22/7) × (2.8)
2
A = 24.64 cm
2
(iii) Given diameter = 7 km
Therefore radius, r = d/2 = 7/2 = 3.5
We know that area of circle = p r
2
A = (22/7) × (3.5)
2
A = 38.5 km
2
3. The area of a circle is 154 cm
2
. Find the radius of the circle.
Solution:
Given area of the circle = 154 cm
2
A = p r
2
154 = 22/7 r
2
r
2
= (154 × 7)/22
r
2
= 49
r = 7 cm
4. Find the radius of a circle, if its area is
(i) 4 p cm
2
(ii) 55.44 m
2
(iii) 1.54 km
2
Solution:
(i) We know that area of circle = p r
2
Given area = 4 p cm
2
A = p r
2
4 p = p r
2
r
2
= 4
Therefore r = 2 cm
Page 3
1. Find the area of a circle whose radius is
(i) 7 cm
(ii) 2.1 m
(iii) 7 km
Solution:
(i) Given radius = 7 cm
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 cm
2
(ii) Given radius = 2.1 m
We know that area of circle = p r
2
A = (22/7) × (2.1)
2
A = 22/7 × 4.41
A = 13.86 m
2
(iii) Given radius = 7 km
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 km
2
2. Find the area of a circle whose diameter is
(i) 8.4 cm
(ii) 5.6 m
(iii) 7 km
Solution:
(i) Given diameter = 8.4 cm
Therefore radius, r = d/2 = 8.4/2 = 4.2
We know that area of circle = p r
2
A = (22/7) × (4.2)
2
A = 55.44 cm
2
(ii) Given diameter = 5.6 cm
Therefore radius, r = d/2 = 5.6/2 = 2.8
We know that area of circle = p r
2
A = (22/7) × (2.8)
2
A = 24.64 cm
2
(iii) Given diameter = 7 km
Therefore radius, r = d/2 = 7/2 = 3.5
We know that area of circle = p r
2
A = (22/7) × (3.5)
2
A = 38.5 km
2
3. The area of a circle is 154 cm
2
. Find the radius of the circle.
Solution:
Given area of the circle = 154 cm
2
A = p r
2
154 = 22/7 r
2
r
2
= (154 × 7)/22
r
2
= 49
r = 7 cm
4. Find the radius of a circle, if its area is
(i) 4 p cm
2
(ii) 55.44 m
2
(iii) 1.54 km
2
Solution:
(i) We know that area of circle = p r
2
Given area = 4 p cm
2
A = p r
2
4 p = p r
2
r
2
= 4
Therefore r = 2 cm
(ii) We know that area of circle = p r
2
Given area = 55.44 cm
2
A = p r
2
55.44 = p r
2
r
2
= (55.44 × 7)/22
r
2
= 17.64 m
r = 4.2 m
(iii) We know that area of circle = p r
2
Given area = 1.54 km
2
A = p r
2
1.54 = p r
2
r
2
= (1.54 × 7)/22
r
2
= 0.49 km
r = 0.7 km
r = 700m
5. The circumference of a circle is 3.14 m, find its area.
Solution:
Given circumference = 3.14m
We know that circumference of circle = 2 p r
3.14 = 2 × 3.14 × r
r = 3.14/ (2 × 3.14)
r = 0.5
We know that area of circle = p r
2
A = (22/7) × (0.5)
2
A = 0.785 m
2
6. If the area of a circle is 50.24 m
2
, find its circumference.
Solution:
Given area of a circle is 50.24 m
2
We know that area of circle = p r
2
50.24 = (22/7) × r
2
r
2
= (50.24 × 7)/22
r
2
= 15.985
Page 4
1. Find the area of a circle whose radius is
(i) 7 cm
(ii) 2.1 m
(iii) 7 km
Solution:
(i) Given radius = 7 cm
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 cm
2
(ii) Given radius = 2.1 m
We know that area of circle = p r
2
A = (22/7) × (2.1)
2
A = 22/7 × 4.41
A = 13.86 m
2
(iii) Given radius = 7 km
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 km
2
2. Find the area of a circle whose diameter is
(i) 8.4 cm
(ii) 5.6 m
(iii) 7 km
Solution:
(i) Given diameter = 8.4 cm
Therefore radius, r = d/2 = 8.4/2 = 4.2
We know that area of circle = p r
2
A = (22/7) × (4.2)
2
A = 55.44 cm
2
(ii) Given diameter = 5.6 cm
Therefore radius, r = d/2 = 5.6/2 = 2.8
We know that area of circle = p r
2
A = (22/7) × (2.8)
2
A = 24.64 cm
2
(iii) Given diameter = 7 km
Therefore radius, r = d/2 = 7/2 = 3.5
We know that area of circle = p r
2
A = (22/7) × (3.5)
2
A = 38.5 km
2
3. The area of a circle is 154 cm
2
. Find the radius of the circle.
Solution:
Given area of the circle = 154 cm
2
A = p r
2
154 = 22/7 r
2
r
2
= (154 × 7)/22
r
2
= 49
r = 7 cm
4. Find the radius of a circle, if its area is
(i) 4 p cm
2
(ii) 55.44 m
2
(iii) 1.54 km
2
Solution:
(i) We know that area of circle = p r
2
Given area = 4 p cm
2
A = p r
2
4 p = p r
2
r
2
= 4
Therefore r = 2 cm
(ii) We know that area of circle = p r
2
Given area = 55.44 cm
2
A = p r
2
55.44 = p r
2
r
2
= (55.44 × 7)/22
r
2
= 17.64 m
r = 4.2 m
(iii) We know that area of circle = p r
2
Given area = 1.54 km
2
A = p r
2
1.54 = p r
2
r
2
= (1.54 × 7)/22
r
2
= 0.49 km
r = 0.7 km
r = 700m
5. The circumference of a circle is 3.14 m, find its area.
Solution:
Given circumference = 3.14m
We know that circumference of circle = 2 p r
3.14 = 2 × 3.14 × r
r = 3.14/ (2 × 3.14)
r = 0.5
We know that area of circle = p r
2
A = (22/7) × (0.5)
2
A = 0.785 m
2
6. If the area of a circle is 50.24 m
2
, find its circumference.
Solution:
Given area of a circle is 50.24 m
2
We know that area of circle = p r
2
50.24 = (22/7) × r
2
r
2
= (50.24 × 7)/22
r
2
= 15.985
r = 3.998 m
We know that circumference of circle = 2 p r
C = 2 × (22/7) × 3.998
C = 25.12 m
7. A horse is tied to a pole with 28 m long string. Find the area where the horse can
graze. (Take p = 22 / 7).
Solution:
Given the length of the string = 28m
The area over which the horse can graze is the same as the area of circle of radius 28 m
Hence required area = p r
2
A = (22/7) × (28)
2
A = 2464 m
2
8. A steel wire when bent in the form of a square encloses an area of 121 cm
2
. If the
same wire is bent in the form of a circle, find the area of the circle.
Solution:
Given area of the square = 121 cm
2
(Side)
2
= 121
Therefore side = 11 cm
We know that the perimeter of the square = 4 (side)
= 4 (11)
= 44 cm
According to the question circumference of the circle = perimeter of the square
So let r be the radius of the circle
2 p r = 44
2 × (22/7) × r = 44
Therefore r = 7 cm
We know that area of the circle = p r
2
A = (22/7) × (7)
2
A = 154 cm
2
9. A road which is 7 m wide surrounds a circular park whose circumference is 352 m.
Find the area of road.
Page 5
1. Find the area of a circle whose radius is
(i) 7 cm
(ii) 2.1 m
(iii) 7 km
Solution:
(i) Given radius = 7 cm
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 cm
2
(ii) Given radius = 2.1 m
We know that area of circle = p r
2
A = (22/7) × (2.1)
2
A = 22/7 × 4.41
A = 13.86 m
2
(iii) Given radius = 7 km
We know that area of circle = p r
2
A = (22/7) × 7
2
A = 22 × 7
A = 154 km
2
2. Find the area of a circle whose diameter is
(i) 8.4 cm
(ii) 5.6 m
(iii) 7 km
Solution:
(i) Given diameter = 8.4 cm
Therefore radius, r = d/2 = 8.4/2 = 4.2
We know that area of circle = p r
2
A = (22/7) × (4.2)
2
A = 55.44 cm
2
(ii) Given diameter = 5.6 cm
Therefore radius, r = d/2 = 5.6/2 = 2.8
We know that area of circle = p r
2
A = (22/7) × (2.8)
2
A = 24.64 cm
2
(iii) Given diameter = 7 km
Therefore radius, r = d/2 = 7/2 = 3.5
We know that area of circle = p r
2
A = (22/7) × (3.5)
2
A = 38.5 km
2
3. The area of a circle is 154 cm
2
. Find the radius of the circle.
Solution:
Given area of the circle = 154 cm
2
A = p r
2
154 = 22/7 r
2
r
2
= (154 × 7)/22
r
2
= 49
r = 7 cm
4. Find the radius of a circle, if its area is
(i) 4 p cm
2
(ii) 55.44 m
2
(iii) 1.54 km
2
Solution:
(i) We know that area of circle = p r
2
Given area = 4 p cm
2
A = p r
2
4 p = p r
2
r
2
= 4
Therefore r = 2 cm
(ii) We know that area of circle = p r
2
Given area = 55.44 cm
2
A = p r
2
55.44 = p r
2
r
2
= (55.44 × 7)/22
r
2
= 17.64 m
r = 4.2 m
(iii) We know that area of circle = p r
2
Given area = 1.54 km
2
A = p r
2
1.54 = p r
2
r
2
= (1.54 × 7)/22
r
2
= 0.49 km
r = 0.7 km
r = 700m
5. The circumference of a circle is 3.14 m, find its area.
Solution:
Given circumference = 3.14m
We know that circumference of circle = 2 p r
3.14 = 2 × 3.14 × r
r = 3.14/ (2 × 3.14)
r = 0.5
We know that area of circle = p r
2
A = (22/7) × (0.5)
2
A = 0.785 m
2
6. If the area of a circle is 50.24 m
2
, find its circumference.
Solution:
Given area of a circle is 50.24 m
2
We know that area of circle = p r
2
50.24 = (22/7) × r
2
r
2
= (50.24 × 7)/22
r
2
= 15.985
r = 3.998 m
We know that circumference of circle = 2 p r
C = 2 × (22/7) × 3.998
C = 25.12 m
7. A horse is tied to a pole with 28 m long string. Find the area where the horse can
graze. (Take p = 22 / 7).
Solution:
Given the length of the string = 28m
The area over which the horse can graze is the same as the area of circle of radius 28 m
Hence required area = p r
2
A = (22/7) × (28)
2
A = 2464 m
2
8. A steel wire when bent in the form of a square encloses an area of 121 cm
2
. If the
same wire is bent in the form of a circle, find the area of the circle.
Solution:
Given area of the square = 121 cm
2
(Side)
2
= 121
Therefore side = 11 cm
We know that the perimeter of the square = 4 (side)
= 4 (11)
= 44 cm
According to the question circumference of the circle = perimeter of the square
So let r be the radius of the circle
2 p r = 44
2 × (22/7) × r = 44
Therefore r = 7 cm
We know that area of the circle = p r
2
A = (22/7) × (7)
2
A = 154 cm
2
9. A road which is 7 m wide surrounds a circular park whose circumference is 352 m.
Find the area of road.
Solution:
Given circumference of park = 352 m
But we know that circumference of circle = 2 p r = 352 m
2 × (22/7) × r = 352
r = (352 × 7)/ 44
r = 56 m
Radius of the path including the 7m wide road = (r + 7) = 56 + 7 = 63m
Therefore area of the road = p × (63)
2
- p × (56)
2
A = 22/7 × 63 × 63 – (22/7) × 56 × 56
A = 22 (9 × 63 – 8 × 56)
A = 22 (567 – 448)
A = 2618 m
2
10. Prove that the area of a circular path of uniform width h surrounding a circular
region of radius r is ph (2r + h).
Solution:
Let radius of circular region = r
Radius of circular path of uniform width h surrounding the circular region of radius,
r = r + h
Therefore area of path = p (r + h)
2
– pr
2
= p r
2
+ p h
2
+ 2 p r h – p r
2
= p h (2r + h)
Hence the proof.
11. The perimeter of a circle is 4pr cm. What is the area of the circle?
Solution:
Given perimeter of circle = 4pr cm
Which can be written as = 2 p (2r)
We know that the perimeter of a circle = 2 p r
Therefore we have radius = 2r
We also know that area of circle = p r
2
= p (2r)
2
= 4 p r
2
cm
2
12. A wire of 5024 m length is in the form of a square. It is cut and made a circle. Find
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