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!
1. What are the Different Types of Circles?
Ans. In mathematical geometry of areas related to circles, they can be of various types, such as orthogonal, tangent, concentric, and congruent ones. Tangent circles consist of two or more round-shaped figures that intersect each other at a single point.
Concentric circles comprise of two or more circles having an identical centre at the same point. However, these circles have two different radiuses. Congruent circles comprise of two or more circles having a similar radius, but they have different central points.
Orthogonal circles have two circles intersecting each other at 90-degree angles. Read area related to circles class 10 solutions for getting a vivid idea of concepts related to circles.
2. What are the Formulas Related to Circles?
Ans. Circles have points of tangency, a specific area, perimeter and diameter. There are specific formulas related to circle related to it. These are as follows:
The diameter of a circle equals to D = 2 * r (where r is equal to the radius of a circle, and D represents its diameter).
Circumference or perimeter of a round-shaped figure will be C = 2 * π * r (here, π stands for the ratio of a circle’s perimeter to its diameter, and r represents the circle’s diameter).
Area of the circle equals to A = π * r2 (where an area comprises of its radius and Pi).
3. What are the Various Parts of a Circle?
Ans. A circle is a figure without any corners or a specific edge. In a segment of mathematics, geometry, circles can be closed or may have a two-dimensional shape of a curve.
A circle comprises of various segments, such as radius, chord, diameter, secant, tangent, to name a few. The radius of a circle is the space from its centre to its outer rim, whereas chord comprises of a line segment having endpoints on the circle. Secants are a line that intersects the circle with two points, whereas tangent intersects the circle at a specific point. You can go through ex 12.3 class 10 maths NCERT to understand circles better!
4. What do you Mean by Area, Perimeter, Diameter and Quadrant of a Circle?
Ans. Circumference or perimeter of a circle gets measured as the distance surrounding the circle. The distance around the circle from its central point is known as diameter. The Greek letter π (Pi) represents the ratio of a circle’s circumference to its diameter. The quadrant of a circle shows its one-fourth section. Read all area related to circle class 10 formulas carefully.
The area represents the number of square units within the space of a circle. The formula of area related to circle is as follows:
A = π * r * r
Where, A = area related to circles, and r represents its radius.