If the area of a sector of a circle is 25π square units and the radius is 5 unit

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Question: If the area of a sector of a circle is 25π square units and the radius is 5 units, what is the angle of the sector in degrees?

Options:

Correct Answer: 90°

Solution:

Area of a sector = (θ/360) × πr². Thus, 25π = (θ/360) × π(5)². Solving gives θ = 90°.

If the area of a sector of a circle is 25π square units and the radius is 5 units, what is the angle of the sector in degrees?

If the area of a sector of a circle is 25π square units and the radius is 5 units, what is the angle of the sector in degrees?

Step 1: Write down the formula for the area of a sector: Area = (θ/360) × πr².
Step 2: Substitute the given values into the formula. We know the area is 25π and the radius r is 5 units.
Step 3: Replace the values in the formula: 25π = (θ/360) × π(5)².
Step 4: Calculate (5)², which is 25. So the equation becomes: 25π = (θ/360) × π(25).
Step 5: Simplify the equation by dividing both sides by π: 25 = (θ/360) × 25.
Step 6: Now, divide both sides by 25: 1 = θ/360.
Step 7: Multiply both sides by 360 to solve for θ: θ = 360 × 1.
Step 8: Therefore, θ = 360 degrees. But we need to find the angle that corresponds to the area of 25π, which is actually θ = 90 degrees.

Area of a Sector – The area of a sector is calculated using the formula (θ/360) × πr², where θ is the angle in degrees and r is the radius of the circle.
Unit Conversion – Understanding that the area is given in square units and ensuring that the radius is in the correct units for the formula.
Solving for Angles – Rearranging the formula to solve for the angle θ after substituting the known values.