CBSE 10
CBSE 10 Mensuration: Everything You Should Know about Circles (Detailed Formulas)
Aha
May 16, 2024
Aha
Language
English
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In this article, we will cover all the necessary information and provide detailed explanations to help you master this topic.
Areas related to circles is a crucial topic in mathematics that deals with finding the area of various shapes and figures that are based on circles. It is essential to understand the properties of circles and their parts to solve problems related to areas of circles.
The area of a circle is the amount of space it occupies in a two-dimensional plane. The formula to calculate the area of a circle is given by:
Area of a circle = πr²
where r is the radius of the circle.
The circumference of a circle is the distance around it. The formula to calculate the circumference of a circle is given by:
Circumference of a circle = 2πr
where r is the radius of the circle.
The angle of a sector of a circle is the angle formed by two radii and an arc. It is measured in degrees.
A sector of a circle is a part of the circle enclosed between two radii and an arc. The formula to calculate the area of a sector of a circle is given by:
Area of a sector of a circle = (θ/360)πr²
where θ is the angle of the sector in degrees and r is the radius of the circle.
The length of an arc of a sector of a circle is the distance along the arc from one end to the other. The formula to calculate the length of an arc of a sector of a circle is given by:
Length of an Arc of a Sector = (θ/360)2πr
where θ is the angle of the sector in degrees and r is the radius of the circle.
A segment of a circle is a part of the circle that is enclosed between a chord and an arc. The formula to calculate the area of a segment of a circle is given by:
Area of a segment of a circle = (θ/360)πr² - (1/2)r²sin θ
where θ is the angle of the sector in degrees, r is the radius of the circle, and s is the length of the arc.
The area of a triangle can be calculated using the following formula:
Area of a triangle = (1/2)bh
where b is the base and h is the height.
Here is a list of all the formulas we have covered so far:
Areas of different plane figures can be calculated using various formulas. It is important to understand the properties of each figure and use the appropriate formula to calculate its area.
When two or more plane figures are combined, their areas can be calculated by adding or subtracting the areas of individual figures.
To master areas related to circles, it is essential to practice. Here are some example questions with step-by-step solutions:
Find the area of a circle with a radius of 5 cm.
✅ Solution: Area of a Circle = πr² = π(5)² cm² = 25π cm².
Find the area of a segment of a circle with a radius of 10 cm and an angle of 60 degrees.
✅ Solution: Area of a Segment of a Circle = (θ/360)πr² - (1/2)r²sin θ =
(60/360)π(10)² - (1/2)(10)²sin 60° cm² = 50/3π - 25√3 cm².
The formula for calculating the area of a circle is
Area of a Circle = πr²
where r is the radius of the circle.
Circumference is the distance around a circle, while perimeter refers to the total distance around any closed figure.
The formula to calculate the length of an arc of a sector is
Length of an Arc of a Sector = (θ/360)2πr
where θ is the angle of the sector in degrees and r is the radius of the circle.
The formula for calculating the area of a segment of a circle is
Area of a Segment of a Circle = (θ/360)πr² - (1/2)r²sin θ
where θ is the angle of the sector in degrees, r is the radius of the circle, and s is the length of the arc.
Areas related to circles is a crucial topic in mathematics, and it is essential to understand the properties of circles and their parts to solve problems related to areas of circles. To further practice and improve your skills in mathematics, it is recommended checking out the website Aha AI.
