The area of a sector of a circle is 30 cm² and the radius is 5 cm. What is the a

₹0.0

Question: 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 degrees

Solution:

Area of sector = (θ/360) × πr². Thus, 30 = (θ/360) × 3.14 × 25. Solving gives θ = (30 × 360) / (3.14 × 25) ≈ 72 degrees.

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?

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: Identify the values given in the problem: Area = 30 cm² and radius (r) = 5 cm.
Step 3: Substitute the radius into the formula: Area = (θ/360) × π × (5 cm)².
Step 4: Calculate (5 cm)²: (5 cm)² = 25 cm².
Step 5: Substitute this value back into the formula: Area = (θ/360) × π × 25 cm².
Step 6: Replace π with 3.14 in the formula: Area = (θ/360) × 3.14 × 25 cm².
Step 7: Set the area equal to 30 cm²: 30 = (θ/360) × 3.14 × 25.
Step 8: Multiply both sides by 360 to eliminate the fraction: 30 × 360 = θ × 3.14 × 25.
Step 9: Calculate 30 × 360: 30 × 360 = 10800.
Step 10: Now the equation is: 10800 = θ × 3.14 × 25.
Step 11: Calculate 3.14 × 25: 3.14 × 25 = 78.5.
Step 12: Now the equation is: 10800 = θ × 78.5.
Step 13: Divide both sides by 78.5 to solve for θ: θ = 10800 / 78.5.
Step 14: Calculate 10800 / 78.5 to find θ: θ ≈ 137.5 degrees.
Step 15: Since we need the angle in degrees, we can round it to the nearest whole number if necessary.

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 the relationship between degrees and the area of a circle is crucial for solving problems involving sectors.