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ICSE Class X Math 2015 Paper

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Question : 29 of 52
Marks: +1, -0
Two solid spheres of radii 2 cm2\text{ cm} and 4 cm4\text{ cm} are melted and recast into a cone of height 8 cm8\text{ cm}. Find the radius of the cone so formed.
Solution:  
     Volume of two spheres = Volume of cone   \;\;\text{ Volume of two spheres = Volume of cone }\;
    43π(2)3+  43π(4)3=  13πr2h\;\;\frac{4}{3}\pi (2)^3+\;\frac{4}{3}\pi (4)^3=\;\frac{1}{3}\pi r^2 h
  32+256=r2×8\;32+256=r^2 \times 8
    2888=r2\;\;\frac{288}{8}=r^2
  36=r2\;36=r^2
  r=6 cm.\;r=6\text{ cm} .
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