Water is pulled up from a well in a bucket on a rope . The rope wind on a cylindrical drum of diameter 14cm. It takes 31 turns of the drum to pull the bucket up from the bottom of the well. How deep is the well?
figure the circumference of the drum
The depth of the well is 31 times that distance (approximately)
To find out the depth of the well, we need to first determine the length of rope wound around the cylindrical drum in one complete turn.
The circumference of a cylindrical drum can be calculated using the formula:
C = 2πr
where C is the circumference, and r is the radius of the drum. In this case, the diameter is given, so we need to divide it by 2 to get the radius:
r = 14 cm / 2 = 7 cm
Now, we can calculate the circumference:
C = 2π(7 cm)
C ≈ 14π cm
Since it takes 31 turns to pull the bucket up from the bottom of the well, the total length of the rope wound around the drum in one complete pull is:
Total rope length = 31 × Length of one turn
The length of one turn is equal to the circumference of the drum, so:
Total rope length = 31 × 14π cm
Now, to find the depth of the well, we need to make an assumption that when the bucket is at the bottom of the well, the rope has been entirely unwound from the cylindrical drum (i.e., the rope length is the same as the depth of the well).
Therefore, the depth of the well is equal to the total rope length:
Depth of well = Total rope length = 31 × 14π cm
You can now calculate the decimal approximation using the value of π (pi) as 3.14 or the exact value if desired.