Question

# A solid piece of iron in the form of a cuboid of dimensions $$4 9 cm × 33cm × 24 cm$$, is moulded to form a solid sphere. The radius of the sphere is

A
21cm
B
23cm
C
25cm
D
19cm

Solution

## The correct option is C $$21cm$$ Solid cuboid of iron is moulded into solid sphere.Hence, volume of cuboid and sphere are equal.Sphere is shown in below figure 1,$$r=?$$Cuboid is shown in below figure 2.$$l=49cm$$$$b=33cm$$$$h=24cm$$$$\therefore$$ Volume of sphere (solid) = Volume of cuboid$$\Rightarrow \dfrac{4}{3}\pi r^{3}=l\times b\times h$$$$\Rightarrow r^{3}=\dfrac{l\times b\times h\times3}{4\times\pi}=\dfrac{49\times33\times24\times3\times7}{4\times22}$$$$\Rightarrow r^{3}=7\times7\times7\times3\times3\times3$$$$\Rightarrow r=21cm$$Hence, right option is $$21cm$$ i.e., option A.Mathematics

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