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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
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B
23cm
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C
25cm
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D
19cm
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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.



1764558_1796787_ans_5eed713f8c344c959b496140de74425f.png

Mathematics

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