Calculate the area of a sector with a radius of 5 cm and a central angle of 60 degrees.

1 question

1 item

Q: Calculate the area of a sector with a radius of 5 cm and a central angle of 60 degrees.

Solution: Area = (θ/360) × π × r² = (60/360) × 3.14 × (5 cm)² = 13.09 cm².

Steps: 11

Step 1: Identify the radius of the sector. In this case, the radius (r) is 5 cm.
Step 2: Identify the central angle of the sector. Here, the angle (θ) is 60 degrees.
Step 3: Use the formula for the area of a sector: Area = (θ/360) × π × r².
Step 4: Substitute the values into the formula: Area = (60/360) × π × (5 cm)².
Step 5: Calculate (5 cm)², which is 25 cm².
Step 6: Now substitute this value into the formula: Area = (60/360) × π × 25 cm².
Step 7: Simplify (60/360) to 1/6.
Step 8: Now the formula looks like this: Area = (1/6) × π × 25 cm².
Step 9: Use the value of π as approximately 3.14: Area = (1/6) × 3.14 × 25 cm².
Step 10: Calculate (1/6) × 3.14, which is approximately 0.5233.
Step 11: Now multiply 0.5233 by 25 cm² to get the area: Area ≈ 13.09 cm².