Metal spheres, each of the radius 2 cm,
Question:

Metal spheres, each of the 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.

Solution:

The radius of each of the metallic sphere is 2cm. Therefore, the volume of each metallic sphere is

$V=\frac{4}{3} \pi \times(2)^{3} \mathrm{~cm}^{3}$

The total volume of the 16 spheres is

$V_{1}=16 \times \frac{4}{3} \pi \times(2)^{3} \mathrm{~cm}^{3}$

The internal dimension of the rectangular box is $16 \mathrm{~cm} \times 8 \mathrm{~cm} \times 8 \mathrm{~cm}$. Therefore, the volume of the rectangular box is

$V_{2}=16 \times 8 \times 8 \mathrm{~cm}^{3}$

Therefore, the volume of the liquid is

$V_{2}-V_{1}=16 \times 8 \times 8-16 \times \frac{4}{3} \pi \times(2)^{3}$

$=1024-536.03$

 

$=488$

Hence volume of liquid is $488 \mathrm{~cm}^{3}$

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