A circular room has radius equal to 40 feet. Marble is to be laid on a sector of the room.
What is the area of the sector if the central angle is 45°?
A = pi * r^2
A = 3.14 * 40^2
A = 5,024 sq ft
45/360 = 0.125
5024 * 0.125 = 628 sq ft
1800 feet2
To find the area of the sector, we can follow these steps:
Step 1: Remember the formula for the area of a sector. The formula is:
Area = (θ/360) * π * r^2
Where:
- Area is the area of the sector
- θ is the central angle measure in degrees
- π is a mathematical constant that represents the ratio of a circle's circumference to its diameter (approximately 3.14159)
- r is the radius of the circle
Step 2: Substitute the given values into the formula:
θ = 45° (central angle)
π ≈ 3.14159
r = 40 feet (radius)
Step 3: Plug in the values and calculate:
Area = (45/360) * 3.14159 * 40^2
Simplifying:
Area = (1/8) * 3.14159 * 1600
= 200 * 3.14159
≈ 628.318
Therefore, the area of the sector with a central angle of 45° is approximately 628.318 square feet.