The area of circle PQR with centre o is 72cm2.What is the area of sector POQ if angle POQ=40 degree?

Explain 72/pie

1 answer

The notation "72/pie" means 72 divided by pi (π). This is often used in geometry to represent the area or circumference of a circle, as these measurements involve pi.

Pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14, but has an infinite number of decimal places.

When calculating the area of a circle, we use the formula A = πr^2, where A is the area, π is pi, and r is the radius of the circle. In this case, we are given that the area of circle PQR is 72 cm^2, so we can write:

72 = πr^2

To find the radius r, we can divide both sides of the equation by pi, giving:

72/π = r^2

Taking the square root of both sides, we get:

r = √(72/π)

This is the radius of the circle, which we will need to find the area of the sector POQ.

To find the area of a sector of a circle, we use the formula A = (θ/360)πr^2, where A is the area of the sector, θ is the angle (in degrees) of the sector, and r is the radius of the circle.

In this case, we are given that the angle POQ is 40 degrees, and we have just found the radius to be √(72/π). So we can plug these values into the formula:

A = (40/360)π(√(72/π))^2

Simplifying, we get:

A = (1/9)π(72/π)

The pi term cancels out, leaving:

A = 8

So the area of sector POQ is 8 cm^2.