A solid piece of iron in the form of a cuboid of dimensions 49 cm $\times$ 33 cm $\times$ 24 cm, is moulded to form a solid sphere. The radius of the sphere is ______.

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A solid piece of iron in the form of a cuboid of dimensions 49 cm $\times$ 33 cm $\times$ 24 cm, is moulded to form a solid sphere. The radius of the sphere is 21 cm. Explanation: As we know, Volume of cuboid = lbh Where, l = length, b = breadth and h = height For given cuboid, Length, l = 49 cm Breadth, b = 33 cm Height, h = 24 cm Volume of cube = 49 $\times$ (33) $\times$ (24) cm3 Now, Let the radius of cube be r. As volume of sphere = $\frac{4}{3}$ pir^3 Where r = radius of sphere Also, volume of cuboid = volume of sphere molded So, 49(33)(24) = $\frac{4}{3}$ pir^3 $\Rightarrow$ $\pi$r3 = 29106 $\Rightarrow$ r3 = 29106 xx $\frac{22}{7}$ $\Rightarrow$ r3 = 9261 $\Rightarrow$ r = root(3)(9261) cm = 21 cm Hence, radius of sphere is 21 cm

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