Single correct option
A solid metal cone of base radius 6 cm and height 8 cm is melted and recast into solid spheres of radius 2 cm each. How many spheres are obtained (with no wastage)?
- A. 6
- B. 8
- C. 9
- D. 12
Show answer and solution
Answer: (C) 9
Volume of the cone = (1/3)πr²h = (1/3)π × 36 × 8 = 96π cm³.
Volume of one sphere = (4/3)π × 2³ = 32π/3 cm³.
Number of spheres = 96π ÷ (32π/3) = 96 × 3/32 = 9.
Tip: Cancel π and the common 1/3 at once: (36 × 8)/(4 × 8) = 9.
Volume of one sphere = (4/3)π × 2³ = 32π/3 cm³.
Number of spheres = 96π ÷ (32π/3) = 96 × 3/32 = 9.
Tip: Cancel π and the common 1/3 at once: (36 × 8)/(4 × 8) = 9.
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