Problem:
The radiation emitted by a radioactive source with a half-life of 3 hours is 32 times higher than the safety limit. What is the minimum time required for the radiation to be under the safety limit?

Solution:
To solve this problem, we need to understand the concept of half-life and how it relates to the decay of a radioactive source.

1. Half-Life:
The half-life of a radioactive substance is the time it takes for half of the atoms in a sample to decay. It is a characteristic property of each radioactive material.

2. Radioactive Decay:
Radioactive decay is a random process, meaning we cannot predict when a specific atom will decay. However, on average, the number of atoms that decay in a given time period is proportional to the number of atoms present.

3. Relation between Half-Life and Radioactive Decay:
The rate at which a radioactive substance decays is inversely proportional to its half-life. This means that the shorter the half-life, the faster the decay, and vice versa.

4. Given Information:
- Half-life of the radioactive source: 3 hours
- Radiation emitted by the source: 32 times higher than the safety limit

5. Calculation:
Let's assume the initial radiation emitted by the source is 32x the safety limit. After one half-life (3 hours), the radiation emitted would be halved, i.e., 16x the safety limit.

After 1 half-life:
- Radiation emitted: 16x the safety limit

After another half-life, the radiation emitted would be halved again, i.e., 8x the safety limit.

After 2 half-lives:
- Radiation emitted: 8x the safety limit

Similarly, after 3 half-lives, the radiation emitted would be halved again, i.e., 4x the safety limit.

After 3 half-lives:
- Radiation emitted: 4x the safety limit

We can continue this process until the radiation emitted is below the safety limit.

After 4 half-lives:
- Radiation emitted: 2x the safety limit

After 5 half-lives:
- Radiation emitted: 1x the safety limit

Conclusion:
Since each half-life is 3 hours, the minimum time required for the radiation emitted by the radioactive source to be under the safety limit is 5 half-lives, which is 5 * 3 = 15 hours.

Therefore, the correct answer is option C) 15 hours.