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What is the length of an arc of a circle with a radius of 10 cm and a central an

Practice Questions

Q1
What is the length of an arc of a circle with a radius of 10 cm and a central angle of 90 degrees?
  1. 15.7 cm
  2. 25 cm
  3. 17.5 cm
  4. 20 cm

Questions & Step-by-Step Solutions

What is the length of an arc of a circle with a radius of 10 cm and a central angle of 90 degrees?
  • Step 1: Identify the radius of the circle, which is given as 10 cm.
  • Step 2: Identify the central angle in degrees, which is given as 90 degrees.
  • Step 3: Use the formula for the length of an arc, which is L = (θ/360) * 2πr.
  • Step 4: Substitute the values into the formula: L = (90/360) * 2 * π * 10.
  • Step 5: Simplify the fraction 90/360 to get 1/4.
  • Step 6: Calculate L = (1/4) * 2 * π * 10.
  • Step 7: Multiply 2 * 10 to get 20, so L = (1/4) * 20 * π.
  • Step 8: Calculate (1/4) * 20 to get 5, so L = 5 * π.
  • Step 9: Use the approximate value of π (about 3.14) to find L = 5 * 3.14.
  • Step 10: Calculate 5 * 3.14 to get approximately 15.7 cm.
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