How to Solve Area Problems Involving Circles Efficiently
An Overview on the Areas Related to Circles Class 10
Mathematics involves the study of various interesting concepts, such as geometry, integers, number system, circles etc. The study of areas related to circles is one such engaging mathematical concept.
Circles are a circular figures without any edges. According to geometry, these round-shaped figures can be of three or four types.
You can seek areas related to circles NCERT solutions to score good grades.
Let’s start learning to understand area related to circle class 10 NCERT!
What are Areas Related to Circles?
The areas related to circles represent the number of squares within a circle’s space. If a circle’s every square has an area approximately 1cm2, you need to count all the squares to calculate its area. Geometrically, the area enclosing a circle with radius r equals to πr2.
Tip: Study all formula of area related to circle to solve problems like a pro!
Exercises on Area Related to Circles Class 10 Solutions
Read the following questions with areas related to circles solutions to score better!
1. What will be the circumference and area of a circle given radius 8 cm? (Sums related to class 10 chapter 12 maths)
Solution: Circumference or perimeter of a circle = 2πr
= 2 * 22/7 * 8 = 50.286 cm (approx.)
Area of the circle will be πr2 = 22/7 * 8 * 8 cm2 = 201.143 cm2 (approx.)
2. Suppose, two circles have a radius of 20 cm and 10 cm, respectively. Find the radius of the third circle having a circumference equal to the sum of both circle’s perimeters. (Problem: area related to circle class 10 NCERT)
Solution: Here, we know about the radii of both circles.
From area related to circle all formula, use perimeter’s formula C = 2* π * r
Radius of 1st circle = 20 cm, and radius of 2nd circle = 10 cm.
Assume, the radius of the 3rd circle to be r.
Now, perimeter of 1st circle = 2* π* 20 = 40 π
Circumference of 2nd one = 2* π* 10 = 20 π
Given, 3rd circle’s circumference = perimeter of 1st and 2nd circle.
Radius will be 2 * π * r = (40 + 20) π
r = 60 π /2 π = 30 cm
3. A car has wheels with a diameter of 70cm each. How many revolutions can each wheel finish in 10 minutes, when the car is running at a speed of 60 km/hour? (Problem - area related to circle class 10 questions with solutions)
Solution: We know that the car wheel’s diameter = 70 cm, and its radius = 35 cm.
Distance travelled in one revolution = wheel’s circumference.
Therefore, Perimeter = 2πr = 2*π*35 =70 cm
The car’s speed is 60 km/hour = (60 *100000)/60 cm/min = 1,00,000 cm/min. If the distance covered in 10 minutes, then = 1,00,000*10 = 10,00,000 cm
Let, n = no. of complete revolutions,
If n*distance covered in 1 resolution = distance covered in 10 minutes
Then, n = (10,00,000*7) / (70*22) = 4545.45 (approx.)
So, every wheel will make 4545.45 complete revolutions.
Often, while studying mathematics, pupils face trouble with cumbersome topics. It happens due to lack of proper subject knowledge. For reducing such a crisis, you can take help from areas related to circles class 10 NCERT solutions. Moreover, try seeking area related to circle class 10 extra questions with solutions.
You can also scroll various mathematics topics from Vedantu’s mobile platform to ace your studies!
FAQs on Areas Related to Circles: Easy Explanations & Examples
1. What are the fundamental formulas used in the Class 10 chapter on Areas Related to Circles?
The key formulas essential for this chapter as per the CBSE 2025-26 syllabus are:
- Area of a Circle: A = πr², where 'r' is the radius.
- Circumference of a Circle: C = 2πr, which is the perimeter of the circle.
- Area of a Sector: A = (θ/360°) × πr², where 'θ' is the angle of the sector in degrees.
- Length of an Arc of a Sector: L = (θ/360°) × 2πr.
2. What is the difference between a sector and a segment of a circle?
A sector and a segment are two different regions within a circle. A sector is the area enclosed by two radii and the corresponding arc, resembling a slice of pizza. A segment, on the other hand, is the area enclosed by a chord and the corresponding arc. The key difference is the boundary: a sector is bounded by two radii, while a segment is bounded by a single chord.
3. How is the area of a segment of a circle calculated?
To calculate the area of a segment, you first find the area of the corresponding sector and then subtract the area of the triangle formed by the two radii and the chord. The formula is:
Area of Segment = Area of the Sector – Area of the corresponding Triangle.
For a minor segment, you use the area of the minor sector. For a major segment, you can subtract the area of the minor segment from the total area of the circle (πr²).
4. Why is the angle 'θ' in the sector area formula divided by 360?
The division by 360 in the formula for the area of a sector, (θ/360°) × πr², represents the proportional part of the circle that the sector occupies. A full circle contains 360 degrees. The ratio θ/360° therefore calculates what fraction of the entire circle the sector represents. Multiplying this fraction by the total area of the circle (πr²) gives you the area of just that fractional piece, which is the sector.
5. What are some real-world examples where calculating areas of sectors and segments is important?
Understanding these concepts has many practical applications. For instance:
- Sectors: Calculating the area covered by a lawn sprinkler, determining the amount of glass needed for an arched window, or finding the area swept by a car's windshield wiper.
- Segments: Estimating the cross-sectional area of liquid in a cylindrical pipe, designing arched supports in bridges, or calculating the area of a garden plot bounded by a straight fence and a curved wall.
6. How do you approach problems involving areas of combined plane figures?
Problems with combined figures, such as a square with semicircles attached or a circle with a triangle removed, require a strategic approach. The general method is to break the complex shape down into simpler, known shapes (like circles, squares, triangles, sectors). You then calculate the area of each individual shape and either add or subtract them as needed to find the area of the required region. For example, to find the area of a running track with straight sides and semi-circular ends, you would add the area of the central rectangle to the areas of the two semi-circles.
7. Is the perimeter of a sector the same as the length of its arc? What is a common mistake here?
No, they are not the same, and this is a very common point of confusion. The length of an arc is only the curved part of the sector's boundary. The perimeter of a sector is the total length of its boundary, which includes the arc length plus the lengths of the two radii that form the sector. Therefore, the formula is: Perimeter of Sector = Length of Arc + 2r. Forgetting to add the two radii is a frequent mistake in exams.
