The radius of a circle of angle at centre of 108⁰ and the area of 4620cm²
How to solve it
(108/360) pi R^2 = 4620
To find the radius of a circle with a given central angle and area, you can follow these steps:
Step 1: Recall the formula for the area of a circle:
Area = π * r^2, where r is the radius.
Step 2: Rearrange the formula to solve for the radius:
r = √(Area / π), where Area is the given area of the circle.
Step 3: Substitute the given area into the formula:
r = √(4620 / π).
Step 4: Use the value of π (Pi) as approximately 3.14159:
r = √(4620 / 3.14159).
Step 5: Calculate the square root of the division:
r ≈ √1470.65379.
Step 6: Round the result to an appropriate number of decimal places:
r ≈ 38.315.
Therefore, the radius of the circle is approximately 38.315 cm.
To find the radius of a circle given the angle at the center and the area, you can use the following steps:
1. Recall the formula for the area of a sector of a circle:
Area = (θ/360) * π * r²
where θ is the angle at the center in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
2. Rearrange the formula to solve for the radius (r):
r = √((Area * 360) / (θ * π))
3. Substitute the given values into the formula:
Area = 4620 cm²
θ = 108⁰
π ≈ 3.14159
r = √((4620 * 360) / (108 * 3.14159))
4. Simplify the expression inside the square root:
r = √(1658880 / 340.42446)
5. Perform the division inside the square root:
r ≈ √(4866.66198)
6. Simplify the square root:
r ≈ 69.81 cm
Therefore, the radius of the circle is approximately 69.81 cm.