WAEC 2020 Mathematics · Question 33
The diameter of a sphere is 12 cm. Calculate, correct of the nearest cm, the volume of the sphere, [Take ]
Options
- A.903 cm
- B.904 cm
- C.905 cm
- D.906 cm
Answer: C. 905 cm
Explanation written with AI and checked against the answer key
Analyze the question: We need the volume of a sphere with diameter 12 cm, using π = 22/7, rounded to the nearest cm³. Concept: Volume of a sphere = (4/3)πr³, where r is the radius (half the diameter). Solution: Radius: r = 12 ÷ 2 = 6 cm r³ = 6³ = 216 V = (4/3) × (22/7) × 216 First, (4/3) × 216 = 4 × 72 = 288 V = 288 × 22/7 = 6336/7 6336 ÷ 7 = 905.14... Check: 7 × 905 = 6335, remainder 1, so 905 + 1/7 ≈ 905.14 To the nearest cm³: 905 cm³ Tip: When π = 22/7 is given, look for factors of 7 in the numbers to simplify. Here 7 doesn't divide 216, so you must divide at the end. Do the multiplication of whole numbers first (288 × 22 = 6336), then divide by 7. Also, always halve the diameter before cubing. Using 12 instead of 6 is a common mistake that gives an answer 8 times too large.AI can make mistakes. Report anything that looks wrong.
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