I have a table to complete.Given that points A and B belong to a circle with centre O; If the area of the sector bounded by central angle AOB is 14.13cm squared and the measure of central angle AOB=45cm squared. What is the radius of the disk(cm)and what is the area of the disk(cm squared)
As = (45/360)Ac = 14.13cm^2.
0.125Ac = 14.13,
Ac=113.4cm^2 = Area of disk or circle.
3.14r^2 = 113.4cm^2,
r^2 = 36,
r = 6cm = radius of disk.
To find the radius of the disk and the area of the disk, we need to use the formulas related to circles.
Let's start with finding the radius of the disk.
1. The formula for the area of a sector is given by:
Area of sector = (θ/360) * π * r^2,
where θ is the measure of the central angle and r is the radius of the circle.
Given that the area of the sector bounded by angle AOB is 14.13 cm² and the measure of central angle AOB is 45 degrees (since you mentioned "cm squared" but it should be degrees), we can rewrite the formula as:
14.13 = (45/360) * π * r^2
2. We can simplify the equation:
14.13 = (1/8) * π * r^2
3. Divide both sides of the equation by (1/8) * π to isolate r^2:
r^2 = (14.13 / ((1/8) * π))
r^2 = 14.13 / (1/8) * π
r^2 = 113.04 / π
4. Now, calculate the value of r by taking the square root of both sides of the equation:
r = √(113.04 / π)
r ≈ 5.34 cm (rounded to two decimal places)
Therefore, the radius of the disk is approximately 5.34 cm.
To find the area of the disk:
1. The formula for the area of a circle is given by:
Area of circle = π * r^2
2. Using the obtained value of r (5.34 cm), we can substitute it into the formula:
Area of circle = π * (5.34)^2
Area of circle ≈ 89.79 cm² (rounded to two decimal places)
Therefore, the area of the disk is approximately 89.79 cm².