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 the water filled in the box .

Answer 1

Radius of the glass spheres, r = 2 cm
Dimensions of the cuboidal box =  \[16cm \times 8cm \times 8cm\]

volume of the spheres =  \[V_s = \frac{4}{3}\pi \left( r \right)^3 = \frac{4}{3}\pi \left( 2 \right)^3\]

volume of the cuboidal box =  \[V_c = 16 \times 8 \times 8 = 1024\]

Volume of water in the cuboidal box = Volume of the cuboidal box − Volume of the 16 glass spheres

\[= 1024 - 16 \times \frac{4}{3}\pi \left( 2 \right)^3 \]

\[ = 1024 - 536 . 6\]

\[ = 487 . 6 {cm}^3\]

Hence, the volume of the water in the cuboidal box = 487.6 cm³