Three(cylindrical) steel drums are put together and a steel band is wrapped tightly around the three drums. If the radius of each drum is 2 feet, what is the length of the steel band? (The view of the drums below is from the top, or end of the drums.)
The three drums are in a triangular shape. One drum is on top and two are on bottom. This is by looking at them from the top like a top view.
Thanks!
To find the length of the steel band, we need to calculate the circumference of each drum and add them together.
The formula for the circumference of a circle is:
C = 2πr
Given that the radius of each drum is 2 feet, we can plug in this value into the formula to find the circumference of one drum:
C1 = 2π(2)
C1 = 4π
Since there are three drums, we need to calculate the total length of all three drums:
Total Length = C1 + C2 + C3
Since all three drums are in a triangular shape, the two bottom drums are adjacent to each other, meaning their circumferences will be in contact. So, for the bottom drums, we need to subtract the overlapping circumference once.
The total length of the steel band can be calculated as follows:
Total Length = C1 + 2C2 - 2π(2)
Let's now substitute in the values to calculate the total length of the steel band:
Total Length = 4π + 2(2π) - 2π(2)
Total Length = 4π + 4π - 4π
Total Length = 4π
Therefore, the length of the steel band is 4π feet.
To find the length of the steel band wrapped around the three drums, we need to calculate the circumference of each drum and then add them together.
The circumference of a cylinder can be calculated using the formula C = 2πr, where C is the circumference and r is the radius.
Given that the radius of each drum is 2 feet, we can calculate the circumference as follows:
C = 2πr
= 2π(2)
= 4π
Since we have three drums, we multiply this result by 3 to get the total length of the steel band:
Total length = 4π * 3
= 12π
Therefore, the length of the steel band wrapped tightly around the three drums is 12π feet, or approximately 37.7 feet.