Question

What is the number of spherical balls of $2.5mm$ diameter that can be obtained by melting a semicircular disc of $8cm$ diameter and $2cm$ thickness?

• A. $6144$
• B. $3072$
• C. $1536$
• D. $768$

Answer 1

The correct option is A $6144$

Volume of semi-circular disc
$=(\frac{1}{2}.\pi 4^2)\times 2c{m}^3=16\pi c{m}^3$
Volume of a ball $=\frac{4}{3}\pi .{\left(\frac{5}{4}\right)}^3(mm{)}^3$
Number of balls $=\frac{\text{Volume of disc}}{\text{Volume of a ball}}$
$=\frac{16\pi .10\times 10\times 10\times 64}{\frac{4}{3}\pi .125}$
$=\frac{3}{4}\times 16\times 512=6144$.