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What is the area of a sector of a circle with a radius of 10 cm and a central an

Practice Questions

Q1
What is the area of a sector of a circle with a radius of 10 cm and a central angle of 60 degrees?
  1. 50π/3 cm²
  2. 100π/3 cm²
  3. 25π cm²
  4. 20π cm²

Questions & Step-by-Step Solutions

What is the area of a sector of a circle with a radius of 10 cm and a central angle of 60 degrees?
  • Step 1: Identify the radius of the circle. In this case, the radius (r) is 10 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) * πr².
  • Step 4: Substitute the values into the formula: Area = (60/360) * π(10)².
  • Step 5: Calculate (10)², which is 100.
  • Step 6: Now the formula looks like this: Area = (60/360) * π * 100.
  • Step 7: Simplify (60/360) to (1/6).
  • Step 8: Now the formula is: Area = (1/6) * 100π.
  • Step 9: Multiply (1/6) by 100 to get 100/6, which simplifies to 50/3.
  • Step 10: Therefore, the area of the sector is 50π/3 cm².
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