Area of Circle Sector Segment and Annulus Formulas with Examples
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.
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FAQs on Areas Related to Circles Concepts and Calculations
1. What is the formula for the area of a circle?
The formula for the area of a circle is A = πr², where r is the radius of the circle.
- π (pi) ≈ 3.14 or 22/7
- r is the distance from the center to the boundary
2. How do you find the area of a circle using the diameter?
To find the area using the diameter, use the formula A = π(d/2)², since radius is half of the diameter.
- Step 1: Divide the diameter by 2 to get the radius.
- Step 2: Substitute into A = πr².
3. Why is the area of a circle πr²?
The area of a circle is πr² because it is derived by rearranging the circle into a shape similar to a rectangle with base πr and height r.
- Circumference = 2πr
- Half circumference = πr
- Area ≈ base × height = πr × r = πr²
4. What is the area of a semicircle?
The area of a semicircle is (1/2)πr² because it is half the area of a full circle.
- Formula: (1/2) × πr²
- r = radius of the semicircle
5. What is the area of a quadrant of a circle?
The area of a quadrant is (1/4)πr² because it represents one-fourth of a circle.
- Formula: (1/4) × πr²
- r = radius
6. How do you find the area of a sector of a circle?
The area of a sector is (θ/360) × πr², where θ is the central angle in degrees.
- Step 1: Divide the angle by 360.
- Step 2: Multiply by πr².
7. What is the difference between the area and circumference of a circle?
The area measures the region inside the circle, while the circumference measures the distance around it.
- Area formula: A = πr²
- Circumference formula: C = 2πr
8. How do you find the radius if the area of a circle is given?
To find the radius from the area, use r = √(A/π).
- Step 1: Divide the area by π.
- Step 2: Take the square root of the result.
9. What are the units of area of a circle?
The units of the area of a circle are always square units such as cm², m², or in².
- If radius is in cm → area is in cm².
- If radius is in meters → area is in m².
10. What are common mistakes when calculating the area of a circle?
Common mistakes in finding the area of a circle include using the diameter instead of radius and forgetting to square the radius.
- Using d instead of r in πr²
- Not squaring the radius
- Using incorrect value of π
