Question : Some ice pieces, spherical in shape, of diameter 6 cm are dropped in a cylindrical container containing some juice and are fully submerged. If the diameter of the container is 18 cm and the level of juice rises by 40 cm, then how many ice pieces are dropped in the container?
Option 1: 95
Option 2: 85
Option 3: 80
Option 4: 90
Correct Answer: 90
Solution :
By volume conservation, we can say that the amount of juice displaced by a solid sphere is equal to the volume of spheres being dropped inside the cylindrical container.
⇒ $x(\frac43\pi r^3)=\pi R^2h$, where $x$ is the number of ice pieces, $r$ is the radius of sphere ice pieces = 3 cm, $R$ is the radius of the cylindrical container = 9 cm, and h is the height = 40 cm
⇒ $x\times\frac43\times3^3=9^2\times40$
⇒ $x=\frac{9\times9\times40}{4\times3\times3}$
⇒ $x=90$
Hence, the correct answer is 90.
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