Area and Circumference of a Circle Practice Questions (original) (raw)
Last Updated : 23 Jul, 2025
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=πr 2
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:
AA = πrA2 = π × 42 = 16π ≈ 50.27 cm2
**Area of Circle B:
AB = πrB2 = π×82 = 64π ≈ 201.06 cm2
As AB/AA = 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:
AL = πrL2 = 196π
⇒ rL2 = 196
⇒ rL = √196 = 14 cm
**Area of Smaller Circle:
AS = πrS2 = 49π
⇒ rS2 = 49
⇒ rS = √49 = 7 cm
**Difference in Radii:
Δr = rL − rS = 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.
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