Solved Examples on Circles
Few examples on circles are:
Example 1: If the diameter of a circle is 142.8 mm, then what is the radius of the circle?
Solution:
Diameter = 142.8 mm
By Formula,
Diameter = 2 radius
Radius = (142.8 ÷ 2) = 71.4 mm
Thus, radius of circle is 71.4 mm
Example 2: Distance around a park is 21.98 yd. What is the radius of the park?
Solution:
Circumference of the Park = 21.98 yd
We know that,
Circumference = 2π × Radius
Radius = Circumference / 2π
Radius = 21.98 / 2×3.14 = 3.5
Thus, radius of circle is 3.5 yd
Example 3: Inner circumference of a circular track is 440 m, and the track is 14 m wide. Calculate the cost of levelling the track at 25 rupees/m2.
Solution:
Let radius of inner circle be r m.
Now,
Inner Circumference = 440 m
2πr = 440
2 × 22/7 × r = 440
r = 440 × 744
Inner Radius, r = 70
Width of track = 14 m
Outer radius (R) = Inner Radius(r) + Width = (70 + 14) = 84 m
Area of Track = π(R2− r2)
= π (842 – 702)
= 22/7 × (7056 – 4900)
= 6776 m2
Cost of levelling at 25 rupees per square meter = 6676 × 25 = 169400 Rupees
Thus, cost of levelling track is 169400 Rupees
Example 4: Find the length of the chord of a circle where the radius is 7 cm and the perpendicular distance from the chord to the centre is 4 cm.
Solution:
Given,
- Radius, r = 8 cm
Distance of Chord to Centre, d = 3 cm
Chord Length = 2√(r2 – d2)
= 2√(82 – 32)
= 2√(64 – 9)
= 2√55
= 2 × 7.416
Chord length = 14.83 cm
Thus, length of chord is 14.83 cm
Example 5: If radius of a circle is 5 cm and measure of the angle of the arc is 110˚, what is the length of the arc?
Solution:
Arc Length = (2 × π × r) × angle / 360°
= 2 × 3.14 × 5 × 110/360°
= 9.6 cm
Thus, length of arc is 9.6 cm.
Example 6: If the area of a sector with a radius of 6 cm is 35.4 cm2. Calculate the angle of the sector.
Solution:
Area of Sector = Angle/360° × (π × r × r)
Angle/360° × (π × 6 × 6) = 35.4
Angle = (35.4/36π) × 360° = 112.67°
Thus, angle of sector is, 112.67°
Circles in Maths
Circles in Maths: A circle is a two-dimensional shape where all points on the circumference are the same distance from the centre. In other words, it is a collection of all points in a plane that are the same distance away from a fixed point, called the centre. Its area is equal to pi times the square of its radius.
In this article, you will understand more about circles in math, including their formulas, examples, parts of circles, and practice problems on circles.
Table of Content
- What is a Circle in Maths?
- Circle Definition
- Circle Examples
- How to Draw a Circle?
- Interior and Exterior of Circle
- Parts of Circle
- Center of Circle
- Radius of Circle
- Diameter of Circle
- Chord of Circle
- Tangent of Circle
- Secant of Circle
- Arc of a Circle
- Segment in Circle
- Sector of a Circle
- Properties of Circle
- Circle Formulas
- Area of Circle Proof
- Types of Circles
- Solved Examples on Circles
- Practice Problems on Circles in Maths
- MCQs on Circles in Maths