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ICSE Class X Math 2016 Paper

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Question : 7 of 57
Marks: +1, -0
A certain number of metallic cones, each of radius 2 cm2\,\text{cm} and height 3 cm3\,\text{cm} are melted and recast into a solid sphere of radius 6 cm6\,\text{cm}. Find the number of cones.
Solution:  
     Let number of cones   =n\;\; \text{ Let number of cones }\; = n
Volume of cones == Volume of sphere
=  13πr2h×n  =  43πr3= \; \frac{1}{3} \pi r^2 h \times n \; = \; \frac{4}{3} \pi r^3
n×  13π×22×3  =  43π×63n \times \; \frac{1}{3} \pi \times 2^2 \times 3 \; = \; \frac{4}{3} \pi \times 6^3
n  =  2163n \; = \; \frac{216}{3}
n  =72n \; = 72
Hence, no. of cones =72=72
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