Find, correct to three significant figures, the surface area of a sphere if the volume of the sphere

JAMB Mathematics 2023 56 views

Find, correct to three significant figures, the surface area of a sphere if the volume of the sphere is 667.89 cm³ [Take π = 3.14]

  1. 423 cm²
  2. 362 cm²
  3. 369 cm² ✓
  4. 441 cm²

Explanation

Step 1: Write volume formula and find radius
V = (4/3)πr³
667.89 = (4/3) × 3.14 × r³

Step 2: Solve for r³
667.89 = 4.1867 × r³
r³ = 667.89/4.1867
r³ = 159.53

Step 3: Find radius
r = ³√159.53
r ≈ 5.424 cm

Step 4: Calculate surface area
SA = 4πr²
= 4 × 3.14 × (5.424)²
= 4 × 3.14 × 29.42
= 369.4 cm²

Step 5: Round to 3 significant figures
SA ≈ 369 cm²

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