Find the area of the sector of the disk of radius r=15 ft and with arc length s=13 ft.
When I did it it came out to .8666667, is that right or do I have to do 1/(13)(15) to get 1.15384571.
circumference = 2P(15) = 30π
fraction of arc over circumference = 13/30π = .137934
whole area = P(15^2) = 225π
sector = .137934(225π) = 97.5 ft^2
To find the area of the sector of a disk, you need to use the formula:
Area = (θ/360) * π * r^2
where θ is the central angle of the sector in degrees, and r is the radius of the disk.
In this case, the arc length s is given as 13 ft, and the radius r is 15 ft. To find the central angle θ, we can use the ratio of the arc length to the circumference of the entire circle:
θ/360 = s/2πr
Plugging in the given values:
θ/360 = 13/(2π * 15)
To solve for θ, multiply both sides by 360:
θ = (13 * 360) / (2π * 15)
Simplifying further:
θ = 234 / π
Now, we can substitute θ and r back into the area formula to find the area of the sector:
Area = (234 / π) / 360 * π * (15)^2
Simplifying further:
Area = (234 * 15^2) / 360
Area = (234 * 225) / 360
Area = 14940 / 360
Area ≈ 41.5 ft^2 (rounded to one decimal place)
Therefore, the correct answer for the area of the sector of the disk is approximately 41.5 ft^2.