Multiple choice

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 filled with preservative liquid. Find the volume of this liquid. (Give the answer to the nearest integer value)

  1. $482 cm^3$
  2. $478 cm^3$
  3. $488 cm^3$
  4. $490 cm^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of box = 16 * 8 * 8 = 1024 cm^3. Volume of 16 spheres = 16 * (4/3) * pi * (2^3) = 16 * (4/3) * 3.14159 * 8 = 536.16 cm^3. Liquid volume = 1024 - 536.16 = 487.84, which rounds to 488.

AI explanation

The volume of the rectangular box is the product of its dimensions, giving 16 * 8 * 8 = 1024 cubic cm. Using the formula for the volume of a sphere, each sphere with a radius of 2 cm has a volume of (4/3) * pi * 2^3 = 33.510 cubic cm. For 16 spheres, the total volume is 16 * 33.510 = 536.16 cubic cm. Subtracting this from the box's total volume gives the liquid volume as 1024 - 536.16 = 487.84 cubic cm, which is 488 cubic cm when rounded to the nearest integer.

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