Multiple choice

$16$ 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 water filled in the box.

  1. $487.6$ $cm^3$
  2. $287.6$ $cm^3$
  3. $47.6$ $cm^3$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of the box is 16 * 8 * 8 = 1024 cm^3. The volume of 16 spheres with radius 2 cm is 16 * (4/3 * pi * 2^3) = 16 * (32/3 * pi) = 512/3 * pi, which is approximately 536.17 cm^3. Subtracting this from the box volume gives 1024 - 536.17 = 487.83 cm^3, which is closest to 487.6 cm^3.

AI explanation

The volume of the cuboidal box is 16 cm times 8 cm times 8 cm, giving 1024 cm^3. Using the sphere volume formula, the total volume of the 16 glass spheres is 16 times (4/3)π(2)^3, which is approximately 536.38 cm^3. Subtracting the spheres' volume from the box volume gives 1024 - 536.38 = 487.62 cm^3. Therefore, the volume of water filled in the box is 487.6 cm^3.

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