2023 · Q112
There are seven hemispherical containers of radius R metres each and each of them is fully filled with water. The water in these is transferred to a hemispherical container of radius equal to 1.5 times of R such that a maximum number of smaller containers get emptied out. How many smaller containers remain fully filled when the larger container gets fully filled?
General Mental Ability, Quantitative Aptitude and StatisticsNumber system and arithmetic
- A5
- B3
- C4
- D2
Explanation
A hemisphere's volume scales with the cube of its radius, so the large container holds (1.5)^3 = 3.375 small-container volumes. Filling it fully consumes 3 full small containers plus part of a fourth, so 4 small containers are touched and 7 - 4 = 3 remain fully filled. Hence B.