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Surface Areas and Volumes — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSSurface Areas and Volumes3 Marks
Question
Metal spheres, each of radius $2\ cm$, are packed into a rectangular box of internal dimensions $16\ cm \times 8\ cm \times 8\ cm.$ 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. $[\text{Use }\pi=3.14]$
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Answer

Internal volume of a rectangular box $= 16\ cm \times 8\ cm \times 8\ cm $
$=1024\ cm^3$
Volume of a sphere$=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times3.14\times(2)^3$
$=\frac{100.48}{3}$
$=33.49\text{ cm}^3$
Volume of $16$ such spheres $=(33.49\times16)\text{ cm}^3$
$=535.84\text{ cm}^3$
Where $16$ spheres are packed, the box is filled with preservative liquid.
Volume of the preservative liquid $=1024-535.84\text{ cm}^3$
$=488.16\text{ cm}^3$

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