Metal spheres, each of radius 2 cm, are packed into a rectangular box

1.	Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimension 16 cm × 8 cm × 8 cm when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid.[use π = \(\frac{669}{213}\)]
Answer» Volume of sphere = \(\frac{4}{3}π R^3\) = \(\frac{{4}\times{669} \times{8}}{{3}\times{213}}\) = 33.50 cm³ Volume of 16 spheres = 16 × 33.50 = 536 cm³ Volume of rectangle = 16 cm × 8 cm × 8 cm = 1024 cm³ Volume of this liquid = 1024 cm³– 536 cm³ = 488 cm³

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimension 16 cm × 8 cm × 8 cm when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid.[use π = \(\frac{669}{213}\)]

Answer»

Volume of sphere = \(\frac{4}{3}π R^3\)

= \(\frac{{4}\times{669} \times{8}}{{3}\times{213}}\)

= 33.50 cm³

Volume of 16 spheres = 16 × 33.50

= 536 cm³

Volume of rectangle = 16 cm × 8 cm × 8 cm

= 1024 cm³

Volume of this liquid = 1024 cm³– 536 cm³

= 488 cm³