If the area of a sector of a circle is 25π cm² and the radius is 10 cm, what is

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Question: If the area of a sector of a circle is 25π cm² and the radius is 10 cm, what is the angle of the sector in degrees?

Options:

Correct Answer: 90 degrees

Solution:

Area of a sector = (θ/360) × πr². Thus, 25π = (θ/360) × π(10)². Solving gives θ = 90 degrees.

If the area of a sector of a circle is 25π cm² and the radius is 10 cm, what is the angle of the sector in degrees?

If the area of a sector of a circle is 25π cm² and the radius is 10 cm, 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 cm² and the radius r is 10 cm.
Step 3: Replace the values in the formula: 25π = (θ/360) × π(10)².
Step 4: Calculate (10)², which is 100. So the equation becomes: 25π = (θ/360) × π(100).
Step 5: Simplify the equation by dividing both sides by π: 25 = (θ/360) × 100.
Step 6: To isolate θ, multiply both sides by 360: 25 × 360 = θ × 100.
Step 7: Calculate 25 × 360, which equals 9000. So now we have: 9000 = θ × 100.
Step 8: Divide both sides by 100 to solve for θ: θ = 9000 / 100.
Step 9: Calculate 9000 / 100, which equals 90. Therefore, 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.
Unit Conversion – Understanding that the area is given in cm² and ensuring that all units are consistent throughout the calculation.