SSC CGL Exam > SSC CGL Notes > Quantitative Aptitude > Important Formulas: Circles
Important Formulas: Circles
Circle Formulas
Circle formulas provide a means to calculate various parameters such as area, circumference, and radius of a circle. Different formulas are available for different parameters, which can be expressed as follows:
Where:
- r represents the radius, and
- π is the mathematical constant pi
Other Circle Formulas
Where:
- r is the radius of the circle
- π is the mathematical constant pi.
- θ is the central angle (in degrees)
Examples
Q2: Find the circumference of a circle with a radius of 5 cm.
Sol:
Given: Radius (r) = 5 cm
Using the circumference formula C = 2πr, where π ≈ 3.14159:
C = 2 × 3.14159 × 5
⇒ C ≈ 31.4159 cm
Ans: The circumference of the circle is approximately 31.4159 cm.
Q2: Calculate the length of an arc if the radius of an arc is 8 cm and the central angle is 40°.
Sol:
Given:
Radius, r = 8 cm
Central angle, θ = 40°
Arc length = 2πr × (θ/360°)
So, s = 2 × π × 8 × (40°/360°)
⇒ s = 5.582 cm
Therefore, the length of an arc is 5.582 cm.
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FAQs on Important Formulas: Circles
| 1. What are the key formulas related to the area and circumference of a circle? |  |
Ans.The area of a circle is calculated using the formula A = πr², where A represents the area and r is the radius of the circle. The circumference, which is the distance around the circle, is given by the formula C = 2πr or C = πd, where d is the diameter of the circle.
| 2. How do you find the radius of a circle if the area is given? | |
Ans.To find the radius when the area is known, you can rearrange the area formula. Starting from A = πr², you can solve for r by dividing both sides by π, giving r² = A/π. Taking the square root of both sides results in r = √(A/π).
| 3. What is the relationship between the diameter and the radius of a circle? | |
Ans.The diameter of a circle is twice the length of the radius. This relationship can be expressed as d = 2r, where d is the diameter and r is the radius. Conversely, the radius can be found using r = d/2.
| 4. How can one calculate the circumference of a circle if only the diameter is known? | |
Ans.If you know the diameter of the circle, you can calculate the circumference using the formula C = πd. Simply multiply the diameter by π to get the circumference.
| 5. What are the units used in measuring the circumference and area of a circle? | |
Ans.The units for measuring the circumference and area of a circle depend on the units used for the radius. If the radius is measured in meters, the circumference will also be in meters, while the area will be in square meters (m²). Similarly, if the radius is in centimeters, the area will be in square centimeters (cm²) and the circumference in centimeters (cm).
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Apr 19, 2026 Last updated
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