Worksheets on finding Circumference and Area of Circle have problems on diameter, radius, and chord of a circle, circumference of a circle, area of a circle, circumference, and area of a circle, distinguishing between circumference and area of a circle, and so on. Area and Circumference of a Circle Worksheet include step-by-step solutions and formulas for all the problems.
Math Worksheet on Circumference and Area of Circle helps students to develop a strong knowledge of geometry and related concepts. Download the PDF Format of easily accessible Area and Circumference of Circle Worksheets and solve the questions for free.
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Circumference and Area of Circle Worksheets
I. If the circumference of a circular sheet is 321 m, find its area.
Solution:
Given that,
The circumference of a circular sheet is =321 m
we know that circumference of the circle=2πr
321=2πr
2×22/7×r=321 m
r=321 m×7/22×1/2
=51 m
We know that area=πr2
A=22/7 × 51 × 51
=8174 sq m
Therefore, the Area of the circle is 8174 sq m.
II. The area of a circle is 748 cm². Find its circumference.
Solution:
Given that,
The area of a circle is =748 cm²
we know that Area of the circle=πr2
r2=748/22 × 7
=238π
r=\(\sqrt{ 238 }\)
=15.42 cm
circumference=2πr
=2×22/7×15.42 cm
=96.92 cm
Therefore, the Circumference of the circle is 96.92 cm.
III. Find the area of a circle whose circumference is the same as the perimeter of the square of the side 11 cm.
Solution:
Given that,
side of the square=11 cm
The circumference of the circle is the same as the perimeter of the square.
we know that the perimeter of the square is 4× side of a square.
=4(11)=44 cm.
2πr=44 cm
2×22/7×r=44 cm
r=44×7/44
r=7 cm
Area of the circle=πr2
=22/7 × 7 × 7
=154 sq cm
Therefore, the Area of the circle=154 sq cm.
IV. A circular sheet of radius 5 units is cut out from a circle of radius 10 units. Find the area of the remaining sheet?
Solution:
Given that,
The area of the circular sheet with a 5cm radius is,
A=πr2
A=π×5×5
A=25π
The area of the circular sheet with a 10cm radius is,
A=πr2
A=π×10 × 10
A=100π
Since the circle with a radius of 5cm is removed, then the remaining area is,
A= 100π-25π
A=75π
A=75 × 3.14
A=235.5
Therefore, The remaining area is 235.5 sq cm.
V. A thin wire is bent to form a circle. If the length of the wire is 484 meters. What is the area of the circle?
Solution:
Given that,
Length of the wire=484 meters
2πr=484 m
2×22/7×r=484
r=484×7/44
r=77 m
Area of the circle=πr2
=22/7×77×77
=18634 m
Therefore, the Area of the circle is 18634 m.
VI. The ratio of the radii of two circles is 3:7. Find the ratio of their circumferences?
Solution:
Given that,
The ratio of the radii of two circles is =3:7
Let the radius of the first circle be r₁ and the radius of the second circle be r₂.
Circumference of a circle = 2πr
r₁ = 3x
r₂ = 7x
Circumference of the 1st wheel= 2πr₁
= 2π3x
= 6πx
Circumference of the 2nd wheel
= 2πr₂
= 2π7x
= 14πx
Now, the ratio of their circumference
= 6πx/14πx
= 6/14
= 3/7
= 3:7
Hence, the ratio of their circumference is 3:7.
VII. From a rectangular metal sheet of size 20 cm by 40 cm, a circular sheet as big as possible is cut. Find the area of the remaining sheet?
Solution:
Given that,
Size of the rectangular metal sheet=20 cm by 40 cm
Area of rectangle=l×b=20 cm×40 cm=800 sq cm
Area of circle=πr2
we know that DiameterD=2r
r=D/2
A=π(D/2)2
Diameter of largest circle=length of the smallest side of the rectangle.
Here length of smaller side=20
=π(20/2)2
=314.16 sq cm
Remaining Area=800 sq cm – 314.16 sq cm
= 485.84 sq cm.
Therefore, the Area of the remaining sheet is 485.84 sq cm.
VIII. The diameter of the circle is 4.9 cm. What is the circumference of the circle?
Solution:
Given that,
The diameter of the circle is d =4.9 cm
we know that d=2r
r=d/2=4.9/2=2.45
Circumference=2πr
=2 × 22/7 × 2.45
=15.4
Therefore, The circumference of the circle is 15.4.
IX. The radius of a cycle wheel is 56 cm. Find the number of turns required to cover a distance of 1680 m?
Solution:
Given that,
The radius of a cycle wheel is= 56 cm
We know that circumference of the circle=2πr
Circumference of the wheel=2 × 22/7 × 56 cm
=352 cm
=3.52 m
In one rotation, the cycle wheel covers a distance of 3.52 m,
So the number of rotations required to cover a distance of 1680 m is,
=1680/3.52=477
Hence, the number of rotations required is 477.
X. A well of diameter 180 cm has a stone parapet around it. If the length of the outer edge of the parapet is 840 cm, find the width of the parapet?
Solution:
Given that,
Diameter=180 cm
radius=diameter/2=180/2=90 cm
The outer edge of parapet=840 cm
Let radius and diameter of the parapet is R respectively.
Since the length of the outer edge of the parapet =840 cm.
Therefore, 2πR=840cm
2R=840 cm/π
2R=840 cm × 7/22
=267cm
Therefore, R=133 cm
Now, the width of the parapet=( Radius of parapet – Radius of the well)
=(133-90)
=43 cm
Hence, the Width of the parapet is 43 cm.
XI. A storm is expected to hit 5 miles in every direction from a small town. What is the area that the storm will affect?
Solution:
Given that,
Radius=5 miles
We know that A=πr2
A=3.14 ×5miles × 5 miles
=78.5 sq miles
Therefore, the area that the storm will affect is 78.5 sq miles.
XII. A semi-circle-shaped rug has a diameter of 4 ft. What is the area of the rug?
Solution:
Given that,
d = 4 ft
radius=d/2=4 ft/2=2
r = 2 ft
Area of circle = 3.14(2 ft) (2 ft)
Area of Circle = 3.14 × 4 sq ft=12.56 sq ft
Area of semi-circle = 12.56 sq ft ÷ 2;
Area of semi-circle = 6.28 sq ft
Hence, Area of the semi circle is 6.28 sq ft.