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Question

A solid piece of iron in the form a cuboid of dimensions (49 cm × 33 cm × 24 cm) is moulded into a solid sphere. The radius of the sphere is
(a) 19 cm
(b) 21 cm
(c) 23 cm
(d) 25 cm

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Solution

(b) 21 cm
Volume of the cuboid =l×b×h = 49×33×24 cm3
Let the radius of the sphere be r cm.
Volume of the sphere=43πr3

The volume of the sphere and the cuboid are the same.
Therefore,

43πr3=49×33×2443×227×r3=49×33×24
r3=49×33×24×2188r3=21×21×21r3=213r=21 cm

Hence, the radius of the sphere is 21 cm.

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