This question is Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD for class 10.

The surface area of a solid metallic sphere is given. It is melted and recast into smaller spheres of given diameter. You have to find How many such spheres can be obtained?

This is the Question Number 26, Exercise 17.5 of M.L Aggarwal.

Deepak BoraNewbie

# The surface area of a solid metallic sphere is 616 cm square. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?

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Given surface area of the sphere = 616 cm^{2}4R^{2}Â = 6164Ã—(22/7)R^{2}Â = 616R^{2}Â = 616Ã—7/4Ã—22R^{2}Â = 49R = 7Volume of the solid metallic sphere = (4/3)R^{3}= (4/3)Ã—7^{3}= (1372/3) cm^{3}Diameter of smaller sphere = 3.5 cmSo radius, r = 3.5/2 = 7/4 cmVolume of the smaller sphere = (4/3)r^{3}= (4/3)Ã—(7/4)^{3}= (343/48) cm^{3}Number of spheres made = Volume of the solid metallic sphere/ Volume of the smaller sphere= (1372/3) Ã·(343/48)=1372Ã—48/(3Ã—343)= 64Hence the number of spheres made is 64.