Question

Question 1
Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions $16cm\times 8cm\times 8cm$. when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. $[use\pi =3.14]$

Answer 1

Given, radius of each metal sphere = 2 cm
Internal dimensions of a rectangular box,
l = 16 cm, b = 8 cm and h = 8 cm
$\therefore$ Volume of a metallic sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\times 3.14\times (2{)}^3$
$=\frac{4}{3}\times 3.14\times 8$
Now, volume of 16 metallic spheres $=\frac{4\times 3.14\times 8\times 16}{3}=\frac{100.48\times 16}{3}$
$=\frac{1607.68}{3}=535.89c{m}^3$
Internal volume of the rectangular box
$=l\times b\times h=16\times 8\times 8$
$=1024c{m}^3$
$\therefore$ Volume of preservative liquid = 1024 – 535.89
$=488.11c{m}^3\approx 488c{m}^3$
Hence, the volume of preservative liquid when 16 metallic spheres are packed in the rectangular box is $488c{m}^3$.