Question

In a game, each participant has to carry water with a small hemispherical container of radius 3 cm, and then pour the water into a larger hemispherical bowl of radius 9 cm. Find the least number of times a participant must carry water so that the larger bowl is fully filled.​

Answer 1

81 times

Explanation:

The problem is essentially asking for the volume of the two hemispheres. Once the volume of the two hemispheres are found, we can divide the larger hemisphere by the smaller one. That will give the amount of times the smaller volume fits into the larger volume.

The volume of a hemisphere is the volume of a sphere divided by 2. Therefore, the volume of the smaller hemisphere is:

`v = (1)/(2) ((4)/(3) \pi {r}^(3) )`

`v= (1)/(2) ((4)/(3) \pi {3}^(3) )`

`v = 6\pi`

The volme of the larger hemisphere is:

`v = (1)/(2) ( (4)/(3) \pi {9}^(3) )`

`v = 486\pi`

Then:

`(486\pi)/(6\pi) = 81`