Question

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

• A. $21cm$
• B. $23cm$
• C. $25cm$
• D. $19cm$

Answer 1

Answer: (A)

$21cm$

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

$\Rightarrow \frac{4}{3}\pi r^3=l\times b\times h$

$\Rightarrow r^3=\frac{l\times b\times h\times 3}{4\times \pi }=\frac{49\times 33\times 24\times 3\times 7}{4\times 22}$

$\Rightarrow r^3=7\times 7\times 7\times 3\times 3\times 3$

$\Rightarrow r=21cm$

Hence, right option is $21cm$ i.e., option A.