If the area of a sector of a circle is 30 cm² and the radius is 5 cm, what is th

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Question: If the area of a sector of a circle is 30 cm² and the radius is 5 cm, what is the angle of the sector in degrees?

Options:

Correct Answer: 72°

Solution:

Area of a sector = (θ/360) × πr². Thus, 30 = (θ/360) × π × 25. Solving gives θ = (30 × 360)/(25π) ≈ 72°.

If the area of a sector of a circle is 30 cm² and the radius is 5 cm, what is the angle of the sector in degrees?

If the area of a sector of a circle is 30 cm² and the radius is 5 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 known values into the formula. Here, the area is 30 cm² and the radius (r) is 5 cm. So, we have: 30 = (θ/360) × π × (5)².
Step 3: Calculate (5)², which is 25. Now the equation looks like this: 30 = (θ/360) × π × 25.
Step 4: Rearrange the equation to solve for θ. Multiply both sides by 360 to get rid of the fraction: 30 × 360 = θ × π × 25.
Step 5: Calculate 30 × 360, which equals 10800. Now the equation is: 10800 = θ × π × 25.
Step 6: Divide both sides by (25π) to isolate θ: θ = 10800 / (25π).
Step 7: Use a calculator to compute the value of θ. This gives approximately θ ≈ 72°.

Area of a Sector – The area of a sector is calculated using the formula A = (θ/360) × πr², where θ is the angle in degrees and r is the radius.
Unit Conversion – Understanding how to manipulate and convert units, particularly in the context of angles and areas.