Calculate the area of a sector of a circle which subtends an angle of 45 degree at the centre of the circle, radius 14cm.
The area of a sector of a circle is given by:
A = (θ/360)πr²
where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is the constant pi (approximately 3.14).
In this case, θ = 45 degrees and r = 14cm, so we can plug in these values to get:
A = (45/360)π(14)²
A = (1/8)π(196)
A = 24.5π
A ≈ 76.96 cm²
Therefore, the area of the sector is approximately 76.96 cm².
To calculate the area of a sector, you can use the following formula:
Area of Sector = (θ/360) * π * r^2
where θ is the central angle in degrees, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14159.
In this case, the central angle is 45 degrees and the radius is 14 cm. Plugging these values into the formula, we have:
Area of Sector = (45/360) * π * (14 cm)^2
= (1/8) * 3.14159 * (14 cm)^2
= (1/8) * 3.14159 * 196 cm^2
≈ 24.1372 cm^2
Therefore, the area of the sector is approximately 24.1372 square centimeters.