Question

$16$ glass spheres each of radius $2$ cm are packed into a cuboidal box of internal dimensions 16 cm $\times$ 8 cm $\times$ 8 cm and then the box is filled with water. Find the volume of water filled in the box.

• A. $487.6$ $c{m}^3$
• B. $287.6$ $c{m}^3$
• C. $47.6$ $c{m}^3$
• D. None of these

Answer 1

The correct option is A $487.6$ $c{m}^3$

Volume of rectangle box$=lbh=16\left(64\right)=1024c{m}^3$
Volume of 1 sphere$=\frac{4}{3}\pi r^3=33.5238c{m}^3$
Volume of 16 spheres $=16\left(33.5238\right)=536.3808$
Volume of liquid$=1024-536.3808=487.6c{m}^3$