A circle worksheet’s Area and circumference help us know the various concepts and step-by-step methods to solve a problem using formulas with practice work problems.

What is Circle?

A circle is a simple closed shape in Euclidean geometry. It is defined as the set of all points in a plane that are at a given distance (called the radius) from a given point (called the center). Here are some key properties and terms associated with a circle:

• Center: The fixed point from which every point on the circle is equidistant.
• Radius: The distance from the center of the circle to any point on the circle. All radii of a circle are equal.
• Diameter: A chord that passes through the center of the circle, or equivalently, twice the radius. It is the longest distance across the circle.
• Chord: A line segment whose endpoints both lie on the circle.
• Arc: A portion of the circumference of a circle.
• Sector: A region bounded by two radii and an arc.
• Segment: A region bounded by a chord and the arc it subtends.

Area of Circle

The space enclosed by the circle is called the area of the circle. The area of the circle is calculated using the formula:

A=πr²

Where r is the radius of the circle.

Circumference of Circle

The total distance around the circle i.e., perimeter of circle; is called circumference of circle. It can be calculated using the formula:

C = 2πr

Where r is the radius of the circle.

Solved Problems: Area and Circumference of Circle

Problem 1: A circle has a radius of 7 cm. Find its circumference.

Solution:

Using the formula for the circumference:

C = 2πr

Substitute r = 7:

C = 2π × 7 = 14π ≈ 43.98 cm

So, the circumference of the circle is approximately 43.98 cm.

Problem 2: A circle has a radius of 5 meters. Find its area.

Solution:

Using the formula for the area:

A = πr²

Substitute r = 5 m:

A = π × 5² = 25π ≈ 78.54 m²

So, the area of the circle is approximately 78.54 square meters.

Problem 3: A circle has a diameter of 12 inches. Find its circumference and area.

Solution:

First, find the radius. Since the diameter d is 12 inches, the radius r is:

r=d/2 = 10/2 = 6 inches

Circumference:

C = 2πr = 2π × 6 = 12π ≈ 37.68 inches

Area:

A = πr² = π × 6² = 36π ≈ 113.04 in

So, the circumference is approximately 113.04 inches, and the area is approximately 78.54 square inches.

Problem 4: The area of a circle is 50.24 square meters. Find its radius.

Solution:

Using the formula for the area:

A = πr²

We know A = 50.24 m², so:

50.24 = πr²

⇒ r² = 50.24/π

⇒ r² ≈ 16

Take the square root of both sides:

r = √16 = 4 meters

So, the radius of the circle is 4 meters.

Problem 5: The circumference of a circle is 31.4 cm. Find its radius.

Solution:

Using the formula for the circumference:

C = 2πr

We know C = 31.4 cm, so:

31.4 = 2πr

r = 31.4/2π

r ≈ 5 cm

So, the radius of the circle is approximately 5 cm.

Problem 6: A circle has a circumference of 62.8 cm. Find its diameter.

Solution:

Using the formula for the circumference:

C = 2πr

We know C = 62.8 cm. First, find the radius r:

62.8 = 2πr

⇒ r = 62.8/2π

⇒ r = 10 cm

Now, find the diameter ddd:

d = 2r = 2×10 = 20 cm

So, the diameter of the circle is 20 cm.

Problem 7: A circle has a diameter of 14 meters. Find its area.

Solution:

First, find the radius. Since the diameter d is 14 meters, the radius r is:

r = d/2 = 14/2 = 7 meters

Using the formula for the area:

A = πr²

Substitute r = 7 m:

A = π×7² = 49π ≈ 153.94 m²

So, the area of the circle is approximately 153.94 square meters.

Problem 8: The area of a circle is 113.04 square inches. Find its radius.

Solution:

Using the formula for the area:

A = πr²

We know A = 113.04 in², so:

113.04 = πr²

⇒ r² = 113.04/π

⇒ r² ≈ 36

⇒ r = √36 = 6 inches

So, the radius of the circle is 6 inches.

Problem 9: Circle A has a radius of 4 cm, and Circle B has a radius of 8 cm. Compare their areas.

Solution:

Area of Circle A:

A_A = πr_A² = π × 4² = 16π ≈ 50.27 cm²

Area of Circle B:

A_B = πr_B² = π×8² = 64π ≈ 201.06 cm²

As A_B/A_A = 64π/16π = 4

So, Circle B’s area is 4 times that of Circle A.

Problem 10: The area of a larger circle is 196π square cm, and the area of a smaller circle is 49π square cm. Find the radius of both circles and the difference in their radii.

Solution:

Area of Larger Circle:

A_L = πr_L² = 196π

⇒ r_L² = 196

⇒ r_L ​= √196 ​= 14 cm

Area of Smaller Circle:

A_S = πr_S² = 49π

⇒ r_S² = 49

⇒ r_S ​= √49 ​= 7 cm

Difference in Radii:

Δr = r_L − r_S = 14 − 7 = 7 cm

So, the radius of the larger circle is 14 cm, the radius of the smaller circle is 7 cm, and the difference in their radii is 7 cm.

Worksheet: Area and Circumference of Circle

Problem 1: Find the circumference of the circle whose radius is ………

(a) 11 cm

(b) 3.2 cm

Problem 2: Find the area of the circle whose diameter is ………..

(a) 48 cm

(b) 3 cm

Problem 3: If the circumference of a circular sheet is 186 m, find its area.

Problem 4: The area of a circle is 256 cm². Find its circumference.

Problem 5: From a circular sheet of a radius 5 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet.

Problem 6: The diameter of a wheel is 70 cm. How many times the wheel will revolve in order to cover a distance of 110 m?

Problem 7: The ratio of the radii of two wheels is 4 : 5. Find the ratio of their circumference.

Read More,

• Circle
• Radius of Circle
• Diameter of Circle
• Chord of Circle
• Arc of Circle
• Sector of Circle
• Segment of Circle
• Area of Circle
• Circumference of Circle

FAQs: Area and Circumference of a Circle

What is the formula for the circumference of a circle?

The circumference C of a circle is given by:

C = 2πr

Where r is the radius of the circle.

What is the relation between radius and diameter of circle?

Diameter of a circle is twice the length of its radius i.e., d = 2r.

What is the formula for the area of a circle?

The area A of a circle is given by:

A = πr²

Where r is the radius of the circle.

What is π (pi)?

π) is a mathematical constant representing the ratio of a circle’s circumference to its diameter. It is approximately equal to 3.14159.