Question

A solid metallic cube with edge $44$cm is melted and recast to produce small spherical balls of radius $2$cm. Then, _______ balls are produced.

• A. $2500$
• B. $2541$
• C. $2451$
• D. None of A, B and C

Answer 1

Answer: (B)

$2541$

Edge of cube $=44cm\left(\text{Given}\right)$

As we know that volume of cube is given by,

$V={\text{side}}^3$

$\therefore$ Volume of given cube $={\left(44\right)}^3=85184{cm}^3$

Now radius of spherical balls formed $\left(r\right)=2cm$

As we know that the volume of a sphere is given by,

$V=\frac{4}{3}\pi r^3$

$\therefore$ Volume of the spherical balls $=\frac{4}{3}\times \frac{22}{7}\times 2^3=\frac{704}{21}{cm}^3$

Now,

No. of balls formed $=\frac{\text{Volume of cube}}{\text{Volume of spherical balls}}$

$\Rightarrow$ No. of balls $=\frac{85184}{\left(\frac{704}{21}\right)}=\frac{85184\times 21}{704}=2541$

Hence $2541$ balls are produced.

Hence the correct answer is $\left(B\right)2541$.