Circles Class 9th Practice Questions

Oct 13, 2025 by recoveryshake.com 38 views

Understanding Circles: A Comprehensive Guide

Circles are a fundamental concept in mathematics, and understanding them is crucial for students in class 9th. In this article, we will provide you with a comprehensive guide to circles, including practice questions to help you assess your knowledge.

What is a Circle?

A circle is a set of points that are all equidistant from a central point called the center. The distance from the center to any point on the circle is called the radius. The diameter of a circle is the longest distance across the circle, passing through its center.

Properties of a Circle

A circle is a closed figure with no beginning or end.
The center of a circle is the point from which all points on the circle are equidistant.
The radius of a circle is the distance from the center to any point on the circle.
The diameter of a circle is the longest distance across the circle, passing through its center.
The circumference of a circle is the distance around the circle.

Circles Class 9th Practice Questions

Multiple Choice Questions

What is the formula for the area of a circle?
- A) A = πr^2
- B) A = 2πr
- C) A = πd^2
- D) A = 2πd
What is the formula for the circumference of a circle?
- A) C = 2πr
- B) C = πr^2
- C) C = πd
- D) C = 2πd
What is the relationship between the radius and the diameter of a circle?
- A) Radius = diameter
- B) Radius = 2diameter
- C) Diameter = 2radius
- D) Diameter = radius

Short Answer Questions

What is the difference between the radius and the diameter of a circle?
What is the formula for the area of a circle in terms of the diameter?
What is the formula for the circumference of a circle in terms of the radius?

Long Answer Questions

A circle has a radius of 5 cm. Find the area and circumference of the circle.
A circle has a diameter of 10 cm. Find the radius and circumference of the circle.
A circle has an area of 50π cm^2. Find the radius and circumference of the circle.

Fill in the Blanks

The formula for the area of a circle is _______________________.
The formula for the circumference of a circle is _______________________.
The relationship between the radius and the diameter of a circle is _______________________.

Answer Key

Multiple Choice Questions

A) A = πr^2
A) C = 2πr
C) Diameter = 2radius

Short Answer Questions

The radius is the distance from the center to any point on the circle, while the diameter is the longest distance across the circle, passing through its center.
A = πd^2
C = 2πr

Long Answer Questions

Area = 25π cm^2, Circumference = 10π cm
Radius = 5 cm, Circumference = 10π cm
Radius = √(50/π) cm, Circumference = 2√(50/π)π cm

Fill in the Blanks

A = πr^2
C = 2πr
Diameter = 2radius

Conclusion

Frequently Asked Questions About Circles

Q: What is a circle?

A: A circle is a set of points that are all equidistant from a central point called the center. The distance from the center to any point on the circle is called the radius.

Q: What is the difference between the radius and the diameter of a circle?

A: The radius is the distance from the center to any point on the circle, while the diameter is the longest distance across the circle, passing through its center.

Q: What is the formula for the area of a circle?

A: The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

Q: What is the formula for the circumference of a circle?

A: The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

Q: What is the relationship between the radius and the diameter of a circle?

A: The relationship between the radius and the diameter of a circle is Diameter = 2radius.

Q: How do you find the area of a circle when the diameter is given?

A: To find the area of a circle when the diameter is given, you can use the formula A = πd^2, where A is the area and d is the diameter.

Q: How do you find the circumference of a circle when the radius is given?

A: To find the circumference of a circle when the radius is given, you can use the formula C = 2πr, where C is the circumference and r is the radius.

Q: What is the formula for the area of a circle in terms of the diameter?

A: The formula for the area of a circle in terms of the diameter is A = πd^2, where A is the area and d is the diameter.

Q: What is the formula for the circumference of a circle in terms of the radius?

A: The formula for the circumference of a circle in terms of the radius is C = 2πr, where C is the circumference and r is the radius.

Q: How do you find the radius of a circle when the diameter is given?

A: To find the radius of a circle when the diameter is given, you can use the formula r = d/2, where r is the radius and d is the diameter.

Q: How do you find the diameter of a circle when the radius is given?

A: To find the diameter of a circle when the radius is given, you can use the formula d = 2r, where d is the diameter and r is the radius.

Conclusion

Circles are a fundamental concept in mathematics, and understanding them is crucial for students in class 9th. In this article, we provided you with a comprehensive guide to circles, including frequently asked questions and answers. We hope that this article has been helpful in understanding the properties and formulas of circles.

Practice Questions

Multiple Choice Questions

What is the formula for the area of a circle?
- A) A = πr^2
- B) A = 2πr
- C) A = πd^2
- D) A = 2πd
What is the formula for the circumference of a circle?
- A) C = 2πr
- B) C = πr^2
- C) C = πd
- D) C = 2πd
What is the relationship between the radius and the diameter of a circle?
- A) Radius = diameter
- B) Radius = 2diameter
- C) Diameter = 2radius
- D) Diameter = radius

Short Answer Questions

What is the difference between the radius and the diameter of a circle?
What is the formula for the area of a circle in terms of the diameter?
What is the formula for the circumference of a circle in terms of the radius?

Long Answer Questions

A circle has a radius of 5 cm. Find the area and circumference of the circle.
A circle has a diameter of 10 cm. Find the radius and circumference of the circle.
A circle has an area of 50π cm^2. Find the radius and circumference of the circle.

Fill in the Blanks

The formula for the area of a circle is _______________________.
The formula for the circumference of a circle is _______________________.
The relationship between the radius and the diameter of a circle is _______________________.

Answer Key

Multiple Choice Questions

A) A = πr^2
A) C = 2πr
C) Diameter = 2radius

Short Answer Questions

The radius is the distance from the center to any point on the circle, while the diameter is the longest distance across the circle, passing through its center.
A = πd^2
C = 2πr

Long Answer Questions

Area = 25π cm^2, Circumference = 10π cm
Radius = 5 cm, Circumference = 10π cm
Radius = √(50/π) cm, Circumference = 2√(50/π)π cm

Fill in the Blanks

A = πr^2
C = 2πr
Diameter = 2radius