Sample Problems Sector of a Circle
Problem 1: Find the area of the sector for a given circle of radius 5 cm if the angle of its sector is 30°.
Solution:
We have, r = 5 and θ = 30°.
Use the formula A = (θ/360°) × πr2 to find the area.
A = (30/360) × (22/7) × 52
⇒ A = 550/840
⇒ A = 0.65 sq. cm
Problem 2: Find the area of the sector for a given circle of radius 9 cm if the angle of its sector is 45°.
Solution:
We have, r = 9 and θ = 45°.
Use the formula A = (θ/360°) × πr2 to find the area.
A = (45/360) × (22/7) × 92
⇒ A = 1782/56
⇒ A = 31.82 sq. cm
Problem 3: Find the area of the sector for a given circle of radius 15 cm if the angle of its sector is π/2 radians.
Solution:
We have, r = 15 and θ = π/2.
Use the formula A = 1/2 × r2 × θ to find the area.
A = 1/2 × 152 × π/2
⇒ A = 1/2 × 225 × 11/7
⇒ A = 2475/14
⇒ A = 176.78 sq. cm
Problem 4: Find the angle subtended at the centre of the circle if the area of its sector is 770 sq. cm and its radius is 7 cm.
Solution:
We have, r = 7 and A = 770.
Use the formula A = (θ/360°) × πr2 to find the value of θ.
=> 770 = (θ/360) × (22/7) × 72
=> 770 = (θ/360) × 154
=> θ/360 = 5
=> θ = 1800°
Problem 5: Find the area of a circle if the area of its sector is 132 sq. cm and the angle subtended at the centre of the circle is 60°.
Solution:
We have, θ = 60° and A = 132.
Use the formula A = (θ/360°) × πr2 to find the value of θ.
=> 132 = (60/360) × (22/7) × r2
=> 132 = (1/6) × (22/7) × r2
=> r2 = 252
=> r = 15.87 cm
Now, Area of circle = πr2
= (22/7) × 15.87 ×15.87
= 5540.85/7
= 791.55 sq. cm
Problem 6: Calculate the arc length when r = 9 cm and θ = 45°.
Solution:
Given,
- r = 9 cm
- θ = 45°
L = (45/360) × 2π × 9
L = (1/8) × (2 × 22/7) × 9
L = (1/8) × (44/7) × 9
L = (1/8) × 44 × 9
L = 44/8 × 9
L = 99/2 cm (rounded to two decimal places)
Therefore, the arc length of the sector is 49.5 cm.
Important Maths Related Links:
Sector of a Circle
Sector of a Circle is one of the components of a circle like a segment which students learn in their academic years as it is one of the important geometric shapes. The sector of a circle is a section of a circle formed by the arc and its two radii and it is produced when a section of the circle’s circumference and two radii meet at both extremities of the arc. From a slice of pizza to a region between two fan blades, we can see sectors of the circle in our daily lives everywhere.
In this article, we will explore the geometric shape of the sector which is derived from the circle in detail including its areas, perimeter, and all the formulas related to the sector of a circle.
Table of Content
- What is Sector of a Circle?
- Sector of a Circle Definition
- Sector Angle
- Sector of a Circle Examples
- Sector of a Circle Area
- Formula for Area of a Sector
- Derivation of Formula for Area of a Sector
- Area of Minor Sector
- Area of Major Sector
- Arc Length of Sector of a Circle
- Formula for Arc Length of a Sector
- Derivation of Formula for Arc Length of a Sector
- Sector of a Circle Perimeter
- Perimeter of a Sector Formula
- Sample Problems Sector of a Circle
- Summarizing Important Formulas of Sector of a Circle