The answer is: The diameter is 4 centimeters.
The explanation is shown below:
1. The volume of the cylinder is:
Where is the radius (
) and
is the height (
).
Then:
2. The total volume of the 12 spheres is:
3. The volume of the cylinder and the total volume of all the 12 spheres, are equal, therefore:
4. Now, you must solve for the radius:
5. The diameter is:
Answer:
Step-by-step explanation:
In this cross sections problem, we can integrate from -r to +r (so that the integral covers the entire base of the solid).
The formatting for the integral did not let me put -r on the lower bound, so i replaced it with a, just know that a represents -r here.
Evaluating the integral gives use that it is equal to;
Caution: this answer may not meet your needs, but this is the answer I have come up with with the given information.
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