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.
To find the length of the steel band, we need to understand the shape that the band forms when wrapped tightly around the three drums. From the description, we can imagine that the band forms a curved shape that connects the circumference of each drum.
Let's break down the problem step by step:
1. Determine the circumference of each drum:
The circumference of a circle can be calculated by using the formula C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. In this case, the radius of each drum is given as 2 feet, so the circumference of each drum is C = 2π(2) = 4π feet.
2. Calculate the length of the steel band formed by connecting the three drums:
Since the band wraps tightly around the three drums, it forms a curved shape that connects the circumferences of each drum. The length of this curved shape can be calculated by adding up the circumferences of the three drums, as the band follows the outer edges of the drums. Therefore, the length of the band is 4π + 4π + 4π = 12π feet.
3. Simplify the length of the steel band:
Since the value of π is approximately 3.14, we can substitute it in the calculation: 12π ≈ 12(3.14) ≈ 37.68 feet.
So, the length of the steel band is approximately 37.68 feet.