Single correct option
A solid metal cone of base radius 6 cm and height 24 cm is melted and recast into solid spheres, each of radius 3 cm. How many spheres are obtained?
- A. 6
- B. 8
- C. 9
- D. 12
Show answer and solution
Answer: (B) 8
Volume is conserved.
Cone volume = (1/3)π r² h = (1/3)π × 36 × 24 = 288π cm³.
Sphere volume = (4/3)π × 3³ = 36π cm³.
Number of spheres = 288π / 36π = 8.
Tip: Keep π symbolic — it cancels, and so do many other factors if you avoid multiplying out early.
Cone volume = (1/3)π r² h = (1/3)π × 36 × 24 = 288π cm³.
Sphere volume = (4/3)π × 3³ = 36π cm³.
Number of spheres = 288π / 36π = 8.
Tip: Keep π symbolic — it cancels, and so do many other factors if you avoid multiplying out early.
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