Final answer:
To find the area of the sector, you need to know the measure of the central angle. The formula for the area of a sector is A = (θ/360) * π * r^2, where θ is the central angle and r is the radius of the circle. In this case, the area of the sector is 18 times the radius of the circle.
Step-by-step explanation:
To find the area of the sector, we need to know the measure of the central angle (θ) of the sector. The formula for the area of a sector is A = (θ/360) * π * r^2, where θ is the central angle and r is the radius of the circle.
In this case, the arc of the sector is given as 10 units. To find the central angle, we can set up a proportion between the length of the arc and the circumference of the entire circle. Since the circumference of a circle is given by C = 2πr, we have the equation:
10/2πr = θ/360
Simplifying the equation, we get:
θ = (10/2πr) * 360 = 1800/πr
Now we can substitute this value of θ into the formula for the area of the sector to find A:
A = (1800/πr/360) * π * r^2 = 18r
Therefore, the area of the sector is 18 times the radius of the circle.