If the area of a sector of a circle is 20π square units and the radius is 10 uni

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Question: If the area of a sector of a circle is 20π square units and the radius is 10 units, what is the angle of the sector in radians?

Options:

Correct Answer: 2 radians

Solution:

The area of a sector is given by (θ/2) * r². Thus, 20π = (θ/2) * 10². Solving gives θ = 4 radians.

If the area of a sector of a circle is 20π square units and the radius is 10 units, what is the angle of the sector in radians?

If the area of a sector of a circle is 20π square units and the radius is 10 units, what is the angle of the sector in radians?

Step 1: Write down the formula for the area of a sector: Area = (θ/2) * r².
Step 2: Substitute the given values into the formula. We know the area is 20π and the radius (r) is 10 units.
Step 3: Replace r in the formula: 20π = (θ/2) * (10)².
Step 4: Calculate (10)², which is 100. Now the equation is: 20π = (θ/2) * 100.
Step 5: Simplify the equation: 20π = 50θ.
Step 6: To find θ, divide both sides by 50: θ = (20π) / 50.
Step 7: Simplify (20π) / 50 to get θ = (2π) / 5.
Step 8: Convert (2π) / 5 to a decimal if needed, but it is already in radians.

Area of a Sector – The area of a sector of a circle is calculated using the formula A = (θ/2) * r², where θ is the angle in radians and r is the radius.
Units of Measurement – Understanding the relationship between area and the units used, ensuring that the area is expressed in square units.
Solving for Angles – Rearranging formulas to solve for the angle in radians based on given area and radius.