Areas Related to Circles — Practice

Question 1

Find area of circle with radius 7 cm (use π = 22/7).

Accepted Answer

✦ Answer: A = πr² = (22/7) × 49 = 154 cm².

Question 2

Find area of sector with radius 14 cm and angle 60°.

Accepted Answer

Step 1 — Apply formula.
  A_sector = (θ/360°) × πr²
  = (60/360) × (22/7) × 14²
  = (1/6) × (22/7) × 196

Step 2 — Compute.
  = (1/6) × (22 × 28) = (1/6) × 616 = 102.67 cm²
  Or: 308/3 cm²

Step 3 — Alternative.
  = (22/7) × 196 / 6 = 22 × 28 / 6 = 616/6 = 102.67 cm²

✦ Answer: Area = 102.67 cm² (or 308/3 cm²).

Question 3

A rectangular ground is 100 m × 60 m with a semi-circular ring at one end (radius 30 m). Find total area.

Accepted Answer

Step 1 — Rectangle area.
  Rectangle = 100 × 60 = 6000 m²

Step 2 — Semi-circle area.
  Semicircle = (1/2) × π × 30²
  = (1/2) × (22/7) × 900
  = 11 × 900 / 7
  = 9900/7 ≈ 1414.29 m²

Step 3 — Total area.
  Total = 6000 + 1414.29
        = 7414.29 m²

Step 4 — Express.
  Or: 6000 + 450π = 6000 + 450(22/7) = 6000 + 9900/7 = (42000 + 9900)/7 = 51900/7 ≈ 7414.29 m²

✦ Answer: Total area ≈ 7414.29 m² (or 51900/7 m²).

Practice — Areas Related to Circles