A circular sinkhole has a circumference of 75.36 meters. A week later, it has a circumference of 150.42 meters.
a. Estimate the diameter of the sinkhole each week.
The sinkhole is about ? meters the first week.
The sinkhole is about ? meters the second week.
b. How many times greater is the diameter of the sinkhole now compared to the previous week?
To estimate the diameter of the sinkhole, we can use the formula relating the circumference of a circle to its diameter: C = πd.
a. Estimate the diameter of the sinkhole each week:
1. First week: Given that the circumference of the sinkhole is 75.36 meters, we can use the formula C = πd and rearrange it to solve for the diameter (d):
d = C/π = 75.36 / π ≈ 24 meters.
2. Second week: Given that the circumference of the sinkhole is now 150.42 meters, we can again use the formula C = πd and rearrange it to solve for the diameter (d):
d = C/π = 150.42 / π ≈ 48 meters.
Therefore, the sinkhole is about 24 meters in diameter the first week and about 48 meters in diameter the second week.
b. To find the ratio of the diameter of the sinkhole now compared to the previous week, we can divide the current diameter by the previous week's diameter:
Ratio = Current Diameter / Previous Week's Diameter
Ratio = 48 meters / 24 meters = 2.
Therefore, the diameter of the sinkhole now is 2 times greater than the diameter of the sinkhole the previous week.