Question

16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box.

NCERT Class X
Mathematics - Exemplar Problems

Chapter _SURFACE AREAS AND VOLUMES

Answer 1

volume of water=volume of cuboid-volume of 16 spheres

16*8*8-16*4/3*22/7*2*2*2

1024-536.3809

487.62

Answer 2

Answer:

$\red { Volume \: of \: the \: water }$

$\green { = 0.487619\: litres }$

Step-by-step explanation:

$Radius\: of \: each \: glass \: sphere (r)=2\:cm$

$\boxed { \pink { Volume \: of \: a \:sphere = \frac{4}{3} \pi r^{3}}}$

$Dimensions \: of \: a \: cuboid :$

$Length (l) = 16 \:cm ,\\Breadth (b) = 8 \:cm ,\\Height (h) = 8\:cm$

/* According to the problem given,

$\red { Volume \: of \: the \: water }$

$= \blue { Volume \: of \:cuboid }\\-16\times \orange {Volume \: of \: one sphere }$

$\blue {= lbh } - 16\times \orange {\frac{4}{3} \pi r^{3}}$

$= 16\times 8 \times 8 - 16 \times \frac{4}{3} \times {22}{7} \times 2^{3}$

$= 16\times 8 \times 8 ( 1-\frac{11}{21})$

$= 16\times 8 \times 8 ( \frac{21 - 11}{21})$

$= 16\times 8 \times 8 \times \frac{10}{21}$

$= \frac{10240}{21}$

$\green {= 487.619\: cm^{3}}$

$\green { = 0.487619\: litres}$

Therefore.,

$\red { Volume \: of \: the \: water }$

$\green { = 0.487619\: litres }$

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