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=πr^{2
}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=πr^{2}

r^{2}=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=πr^{2}

=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=πr^{2}

A=π×5×5

A=25π

The area of the circular sheet with a 10cm radius is,

A=πr^{2}

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=πr^{2}

=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=πr^{2}

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=πr^{2}

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.

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