The Area Of A Circle PQR with center O Is 72cm2 What Is the area of the sector If POR is 40'
The area of the sector (like a slice of pizza) would be 40/360 of 72 cm^2 or (1/9)(72) cm^2
= ....
To find the area of a sector, you will need to know the angle measure of the sector and the radius of the circle. In this case, we have the angle measure POR as 40' (40 minutes) and the area of the circle as 72 cm².
Step 1: Convert the angle measure to degrees:
Since there are 60 minutes in a degree, 40 minutes is equal to 40/60 = 2/3 degrees.
Step 2: Calculate the radius of the circle:
The area of a circle is given by the formula A = πr². We know that the area of the circle is 72 cm², so we can solve for the radius.
A = πr²
72 = πr²
Dividing both sides of the equation by π:
72/π = r²
r² = 72/π
Taking the square root of both sides:
r = √(72/π)
Step 3: Calculate the area of the sector:
The formula for the area of a sector is given by A = (θ/360) * πr²,
where θ is the angle measure in degrees and r is the radius.
Plugging in the values:
A = (2/3/360) * π * (√(72/π))²
= (2/1080) * π * (72/π)
= (2/1080) * 72
= 0.0666667 * 72
= 4.8 cm²
Therefore, the area of the sector POR is 4.8 cm².
To find the area of the sector POR, you need to know the angle of the sector and the radius of the circle.
1. To find the angle in degrees, convert 40 minutes (') to degrees. Since there are 60 minutes in a degree, divide 40 by 60:
40 / 60 = 0.67 degrees
2. The formula to calculate the area of a sector is A = (θ/360) * π * r^2, where A is the area, θ is the angle in degrees, π is a mathematical constant (approximately 3.14159), and r is the radius of the circle.
3. Rearrange the formula to solve for A:
A = (θ/360) * π * r^2
4. Plug in the given values:
A = (0.67/360) * π * r^2
5. The given information states that the area of the entire circle is 72 cm^2. The formula for the area of a circle is A = π * r^2. Rearrange this formula to solve for r:
r^2 = A/π
r = √(A/π)
6. Plug in the area of the circle to find the radius:
r = √(72/π)
7. Now substitute the value of θ and r in the equation for A:
A = (0.67/360) * π * (√(72/π))^2
8. Simplify the equation:
A = (0.67/360) * π * (72/π)
A = 0.004647 * 72
A ≈ 0.33 cm^2
Therefore, the area of the sector POR is approximately 0.33 cm^2.