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?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 90.
By volume conservation, we can say that the amount of water displaced by a solid sphere is equal to the volume of spheres being dropped inside the cylindrical beaker.
⇒ x × (4π)/3 × r3 = π × R2 × h
x = number of spheres,
r = 3 and R = 9
⇒ x × (4π)/3 × 33 = π × 92 × 40
⇒ x × 4 × 32 = 92 × 40
⇒ x × 4 = 9 × 40
⇒ x = 9 × 10
⇒ x = 90