Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RD Sharma Solutions: Mensuration – I (Area of Circle Exercise 21.1)
Mensuration – I (Area of Circle Exercise 21.1) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download
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Page 1
1. Find the circumference of the circle whose radius is
(i) 14cm
(ii) 10m
(iii) 4km
Solution:
(i) Given radius = 14cm
We know that the circumference of the circle = 2 p r
p value is 22/7
C = 2 × (22/7) × 14
C = 88cm
(ii) Given radius = 10m
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 10
C = 62.86 m
(iii) Given radius = 4km
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 4
C = 25.142 km
2. Find the circumference of a circle whose diameter is
(i) 7 cm
(ii) 4.2 cm
(iii) 11.2 km
Solution:
(i) Given diameter = 7cm
We know that radius = diameter/2
Therefore, r = d/2
r = 7/2
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 7/2
C = 22 cm
Page 2
1. Find the circumference of the circle whose radius is
(i) 14cm
(ii) 10m
(iii) 4km
Solution:
(i) Given radius = 14cm
We know that the circumference of the circle = 2 p r
p value is 22/7
C = 2 × (22/7) × 14
C = 88cm
(ii) Given radius = 10m
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 10
C = 62.86 m
(iii) Given radius = 4km
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 4
C = 25.142 km
2. Find the circumference of a circle whose diameter is
(i) 7 cm
(ii) 4.2 cm
(iii) 11.2 km
Solution:
(i) Given diameter = 7cm
We know that radius = diameter/2
Therefore, r = d/2
r = 7/2
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 7/2
C = 22 cm
(ii) Given diameter = 4.2 cm
We know that radius = diameter/2
Therefore, r = 4.2/2
r = 2.1
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 2.1
C = 13.2 cm
(iii) Given diameter = 11.2 km
We know that radius = diameter/2
Therefore, r = 11.2/2
r = 5.6
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 5.6
C = 35.2 km
3. Find the radius of a circle whose circumference is
(i) 52.8 cm
(ii) 42 cm
(iii) 6.6 km
Solution:
(i) Given circumference, C = 52.8 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (52.8 × 7)/ (2 × 22)
r = 369.6/ 44
r = 8.4 cm
(ii) Given circumference, C = 42 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (42 × 7)/ (2 × 22)
r = 294/ 44
r = 6.68 cm
(iii) Given circumference, C = 6.6 km
Page 3
1. Find the circumference of the circle whose radius is
(i) 14cm
(ii) 10m
(iii) 4km
Solution:
(i) Given radius = 14cm
We know that the circumference of the circle = 2 p r
p value is 22/7
C = 2 × (22/7) × 14
C = 88cm
(ii) Given radius = 10m
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 10
C = 62.86 m
(iii) Given radius = 4km
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 4
C = 25.142 km
2. Find the circumference of a circle whose diameter is
(i) 7 cm
(ii) 4.2 cm
(iii) 11.2 km
Solution:
(i) Given diameter = 7cm
We know that radius = diameter/2
Therefore, r = d/2
r = 7/2
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 7/2
C = 22 cm
(ii) Given diameter = 4.2 cm
We know that radius = diameter/2
Therefore, r = 4.2/2
r = 2.1
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 2.1
C = 13.2 cm
(iii) Given diameter = 11.2 km
We know that radius = diameter/2
Therefore, r = 11.2/2
r = 5.6
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 5.6
C = 35.2 km
3. Find the radius of a circle whose circumference is
(i) 52.8 cm
(ii) 42 cm
(iii) 6.6 km
Solution:
(i) Given circumference, C = 52.8 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (52.8 × 7)/ (2 × 22)
r = 369.6/ 44
r = 8.4 cm
(ii) Given circumference, C = 42 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (42 × 7)/ (2 × 22)
r = 294/ 44
r = 6.68 cm
(iii) Given circumference, C = 6.6 km
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (6.6 × 7)/ (2 × 22)
r = 46.2/ 44
r = 1.05 km
4. Find the diameter of a circle whose circumference is
(i) 12.56 cm
(ii) 88 m
(iii) 11.0 km
Solution:
(i) Given circumference, C = 12.56 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (12.56 × 7)/ (2 × 22)
r = 87.92/ 44
r = 1.99 cm
But diameter = 2r
= 2 × 1.99 = 3.99 cm
(ii) Given circumference, C = 88 m
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (88 × 7)/ (2 × 22)
r = 616/ 44
r = 14 m
But diameter = 2r
= 2 × 14 = 28 m
(iii) Given circumference, C = 11.0 km
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (11 × 7)/ (2 × 22)
r = 77/ 44
r = 1.75 km
But diameter = 2r
Page 4
1. Find the circumference of the circle whose radius is
(i) 14cm
(ii) 10m
(iii) 4km
Solution:
(i) Given radius = 14cm
We know that the circumference of the circle = 2 p r
p value is 22/7
C = 2 × (22/7) × 14
C = 88cm
(ii) Given radius = 10m
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 10
C = 62.86 m
(iii) Given radius = 4km
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 4
C = 25.142 km
2. Find the circumference of a circle whose diameter is
(i) 7 cm
(ii) 4.2 cm
(iii) 11.2 km
Solution:
(i) Given diameter = 7cm
We know that radius = diameter/2
Therefore, r = d/2
r = 7/2
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 7/2
C = 22 cm
(ii) Given diameter = 4.2 cm
We know that radius = diameter/2
Therefore, r = 4.2/2
r = 2.1
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 2.1
C = 13.2 cm
(iii) Given diameter = 11.2 km
We know that radius = diameter/2
Therefore, r = 11.2/2
r = 5.6
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 5.6
C = 35.2 km
3. Find the radius of a circle whose circumference is
(i) 52.8 cm
(ii) 42 cm
(iii) 6.6 km
Solution:
(i) Given circumference, C = 52.8 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (52.8 × 7)/ (2 × 22)
r = 369.6/ 44
r = 8.4 cm
(ii) Given circumference, C = 42 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (42 × 7)/ (2 × 22)
r = 294/ 44
r = 6.68 cm
(iii) Given circumference, C = 6.6 km
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (6.6 × 7)/ (2 × 22)
r = 46.2/ 44
r = 1.05 km
4. Find the diameter of a circle whose circumference is
(i) 12.56 cm
(ii) 88 m
(iii) 11.0 km
Solution:
(i) Given circumference, C = 12.56 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (12.56 × 7)/ (2 × 22)
r = 87.92/ 44
r = 1.99 cm
But diameter = 2r
= 2 × 1.99 = 3.99 cm
(ii) Given circumference, C = 88 m
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (88 × 7)/ (2 × 22)
r = 616/ 44
r = 14 m
But diameter = 2r
= 2 × 14 = 28 m
(iii) Given circumference, C = 11.0 km
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (11 × 7)/ (2 × 22)
r = 77/ 44
r = 1.75 km
But diameter = 2r
= 2 × 1.75 = 3.5 km
5. The ratio of the radii of two circles is 3: 2. What is the ratio of their circumferences?
Solution:
Given that the ratio of the radii = 3: 2
So, let the radii of the two circles be 3r and 2r respectively.
And let C
1
and C
2
be the circumference of the two circles of radii 3r and 2r respectively.
C
1
= 2 p × 3r = 6 p r … (i)
Now C
2
= 2 × 2 p r = 4 p r … (ii)
Consider, C
1
/C
2
= (6 p r)/ 4 p r = 6/4 = 3/2
C
1
: C
2
= 3: 2
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:
Given length of rectangular wire = 18.7 cm
Breadth of rectangular wire = 14.3 cm
According to the question length of wire = perimeter of the rectangle
= 2 (l + b) = 2 × (18.7 + 14.3)
= 2 (33)
= 66 cm
Let the wire bent in the form of circle of radius r cm then we have
Circumference = 66cm
2 p r = 66
2 × (22/7) × r = 66
(44/7) r = 66
r = (66 × 7)/44
r = 462/44
= 10.5 cm
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:
Given side of equilateral triangle = 6.6 cm
Page 5
1. Find the circumference of the circle whose radius is
(i) 14cm
(ii) 10m
(iii) 4km
Solution:
(i) Given radius = 14cm
We know that the circumference of the circle = 2 p r
p value is 22/7
C = 2 × (22/7) × 14
C = 88cm
(ii) Given radius = 10m
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 10
C = 62.86 m
(iii) Given radius = 4km
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 4
C = 25.142 km
2. Find the circumference of a circle whose diameter is
(i) 7 cm
(ii) 4.2 cm
(iii) 11.2 km
Solution:
(i) Given diameter = 7cm
We know that radius = diameter/2
Therefore, r = d/2
r = 7/2
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 7/2
C = 22 cm
(ii) Given diameter = 4.2 cm
We know that radius = diameter/2
Therefore, r = 4.2/2
r = 2.1
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 2.1
C = 13.2 cm
(iii) Given diameter = 11.2 km
We know that radius = diameter/2
Therefore, r = 11.2/2
r = 5.6
We know that the circumference of the circle = 2 p r
C = 2 × (22/7) × 5.6
C = 35.2 km
3. Find the radius of a circle whose circumference is
(i) 52.8 cm
(ii) 42 cm
(iii) 6.6 km
Solution:
(i) Given circumference, C = 52.8 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (52.8 × 7)/ (2 × 22)
r = 369.6/ 44
r = 8.4 cm
(ii) Given circumference, C = 42 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (42 × 7)/ (2 × 22)
r = 294/ 44
r = 6.68 cm
(iii) Given circumference, C = 6.6 km
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (6.6 × 7)/ (2 × 22)
r = 46.2/ 44
r = 1.05 km
4. Find the diameter of a circle whose circumference is
(i) 12.56 cm
(ii) 88 m
(iii) 11.0 km
Solution:
(i) Given circumference, C = 12.56 cm
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (12.56 × 7)/ (2 × 22)
r = 87.92/ 44
r = 1.99 cm
But diameter = 2r
= 2 × 1.99 = 3.99 cm
(ii) Given circumference, C = 88 m
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (88 × 7)/ (2 × 22)
r = 616/ 44
r = 14 m
But diameter = 2r
= 2 × 14 = 28 m
(iii) Given circumference, C = 11.0 km
We know that the circumference of the circle = 2 p r
Therefore radius, r = C/2 p
r = (11 × 7)/ (2 × 22)
r = 77/ 44
r = 1.75 km
But diameter = 2r
= 2 × 1.75 = 3.5 km
5. The ratio of the radii of two circles is 3: 2. What is the ratio of their circumferences?
Solution:
Given that the ratio of the radii = 3: 2
So, let the radii of the two circles be 3r and 2r respectively.
And let C
1
and C
2
be the circumference of the two circles of radii 3r and 2r respectively.
C
1
= 2 p × 3r = 6 p r … (i)
Now C
2
= 2 × 2 p r = 4 p r … (ii)
Consider, C
1
/C
2
= (6 p r)/ 4 p r = 6/4 = 3/2
C
1
: C
2
= 3: 2
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:
Given length of rectangular wire = 18.7 cm
Breadth of rectangular wire = 14.3 cm
According to the question length of wire = perimeter of the rectangle
= 2 (l + b) = 2 × (18.7 + 14.3)
= 2 (33)
= 66 cm
Let the wire bent in the form of circle of radius r cm then we have
Circumference = 66cm
2 p r = 66
2 × (22/7) × r = 66
(44/7) r = 66
r = (66 × 7)/44
r = 462/44
= 10.5 cm
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:
Given side of equilateral triangle = 6.6 cm
Length of the wire = the perimeter of equilateral triangle
Perimeter of equilateral triangle = 3 × side
= 3 × 6.6 = 19.8 cm
Therefore circumference = 19.8 cm
C = 2 p r
19.8 = 2 × (22/7) × r
19.8 = (44/7) r
r = (19.8 × 7)/44
r = 138.6/44
= 3.15 cm
Diameter = 2r
Therefore diameter of ring = 2 × 3.15 = 6.3 cm
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.
Given the diameter of the wheel = 63 cm
We know that circumference of the wheel = p d
= 22/7 x 63
= 198 cm.
Thus, the cycle covers 198 cm in one revolution.
Therefore the distance covered by the cycle in 1000 revolutions = (198 x 1000)
= 198000 cm
= 1980 m.
9. The diameter of a wheel of a car is 98 cm. How many revolutions will it make to
travel 6160 meters.
Solution:
In one revolution of the wheel, the car travels a distance equal to the circumference of
the wheel.
Given diameter of the wheel of a car = 98 cm
Circumference of the wheel of the car = p d
= 22/7 x 98
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FAQs on Mensuration – I (Area of Circle Exercise 21.1) RD Sharma Solutions - Mathematics (Maths) Class 7
| 1. What is the formula for finding the area of a circle? |  |
Ans. The formula for finding the area of a circle is A = πr^2, where A represents the area and r represents the radius of the circle.
| 2. How do I calculate the radius of a circle if I know the area? | |
Ans. To calculate the radius of a circle if you know the area, you can use the formula r = √(A/π), where r represents the radius and A represents the area of the circle.
| 3. Can I use the diameter to find the area of a circle? | |
Ans. Yes, you can use the diameter to find the area of a circle. The formula for finding the area of a circle using the diameter is A = (π/4) × d^2, where A represents the area and d represents the diameter of the circle.
| 4. How can I find the circumference of a circle if I only know the area? | |
Ans. If you only know the area of a circle and want to find the circumference, you can use the formula C = 2√(πA), where C represents the circumference and A represents the area of the circle.
| 5. What is the relationship between the radius and diameter of a circle? | |
Ans. The radius of a circle is half the length of its diameter. In other words, the diameter is twice the length of the radius. So, if you know the radius, you can find the diameter by multiplying it by 2, and vice versa.
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Dec 23, 2024 Last updated |
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