Final answer:
The new circumferences of the circular drop of oil after decreasing the diameter by 5%, 10%, and 15% are 9.5 cm, 8.55 cm, and 7.27 cm respectively.
Step-by-step explanation:
The new diameter of the circular drop of oil can be found by calculating the decrease percentage of each given diameter. Let's calculate: 5% of 10 cm = 0.05 * 10 cm = 0.5 cm. So, the new diameter after the first decrease is 10 cm - 0.5 cm = 9.5 cm. Similarly, the new diameter after the second decrease is 9.5 cm - (0.1 * 9.5 cm) = 8.55 cm, and the new diameter after the third decrease is 8.55 cm - (0.15 * 8.55 cm) = 7.27 cm.
The circumference of the circle can be found using the formula: circumference = 2 * radius. Since the radius is half the diameter, we can calculate:
- For the initial diameter of 10 cm, the radius is 10 cm / 2 = 5 cm. Therefore, the initial circumference is 2 * 5 cm = 10 cm.
- For the new diameter of 9.5 cm, the new radius is 9.5 cm / 2 = 4.75 cm. Therefore, the new circumference is 2 * 4.75 cm = 9.5 cm.
- For the new diameter of 8.55 cm, the new radius is 8.55 cm / 2 = 4.275 cm. Therefore, the new circumference is 2 * 4.275 cm = 8.55 cm.
- For the new diameter of 7.27 cm, the new radius is 7.27 cm / 2 = 3.635 cm. Therefore, the new circumference is 2 * 3.635 cm = 7.27 cm.
So, the new circumferences after each decrease are 9.5 cm, 8.55 cm, and 7.27 cm respectively.
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