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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. What is the volume of water filled in the box?

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487.6 c m 3

490.8cm³

500.2 cm³

650.3 cm³

answer is A.

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Detailed Solution

Given that 16 glass spheres are packed into a cuboidal box and then the box is filled with water.
And the dimension of the cuboid is given as,

16 c m × 8 c m × 8 c m

.
So, volume of the cuboid:

l × b × h = 16 × 8 × 8 = 1024 c m 3

It is also given that, the radius of a glass sphere,

r = 2 c m

.
So, the volume of a glass sphere is,

\frac{4}{3} π r^{3} = \frac{4}{3} \times \frac{22}{7} \times 2^{3}

\Rightarrow \frac{704}{21}

\Rightarrow 33.523 {cm}^{3}

Now, volume of 16 spheres is,

16 × 33.523 = 536.37 c m 3

And required volume of water is calculated as:

\Rightarrow

Therefore, the correct option is 1.

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