Single correct option
A solid metallic sphere of radius 6 cm is melted and recast into solid right circular cones, each of base radius 3 cm and height 4 cm. How many cones are obtained, assuming no wastage?
- A. 24
- B. 48
- C. 36
- D. 12
Show answer and solution
Answer: (A) 24
Volume of sphere = (4/3)π(6)³ = 288π cm³.
Volume of one cone = (1/3)π(3)²(4) = 12π cm³.
Number of cones = 288π / 12π = 24.
Tip: π and the 1/3 factors cancel; compare 4r³ for the sphere with r²h for the cone: 4 × 216 = 864 and 9 × 4 = 36, ratio 24.
Volume of one cone = (1/3)π(3)²(4) = 12π cm³.
Number of cones = 288π / 12π = 24.
Tip: π and the 1/3 factors cancel; compare 4r³ for the sphere with r²h for the cone: 4 × 216 = 864 and 9 × 4 = 36, ratio 24.
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