The figure at the right shows three circular pipes all with 12inch diameters the have been strapped together by a metal band.What is the lenght of the band?
I don't even know where to start , please help?
The centers of the pipes form an equilateral triangle, with sides of length 24.
The belt then consists of three straight segments of length 24, and three arcs of the circles, subtending angles of 2pi/3.
To find the length of the band, we need to calculate the circumference of each pipe and then add them up.
The formula to find the circumference of a circle is C = π * d, where C is the circumference and d is the diameter.
Given that the diameter of each pipe is 12 inches, we can calculate the circumference of each pipe:
Pipe 1: C1 = π * 12 inches
Pipe 2: C2 = π * 12 inches
Pipe 3: C3 = π * 12 inches
Since all three pipes are strapped together by the metal band, the total length of the band is the sum of the circumferences of the three pipes:
Total length = C1 + C2 + C3
Now, let's calculate the total length step by step:
Step 1:
Find the value of π (pi). Pi is an irrational number, but we often approximate it to 3.14.
Step 2:
Calculate the circumference of each pipe.
C1 = π * 12 inches = 3.14 * 12 inches
C2 = π * 12 inches = 3.14 * 12 inches
C3 = π * 12 inches = 3.14 * 12 inches
Step 3:
Add the circumferences of all three pipes to find the total length of the band.
Total length = C1 + C2 + C3
Total length = (3.14 * 12 inches) + (3.14 * 12 inches) + (3.14 * 12 inches)
Step 4:
Perform the multiplication and addition to get the final answer.
Total length = (3.14 * 12 inches) + (3.14 * 12 inches) + (3.14 * 12 inches)
Total length = 37.68 inches + 37.68 inches + 37.68 inches
Total length = 113.04 inches
Therefore, the length of the metal band is 113.04 inches.
To determine the length of the metal band, we need to calculate the circumference of each individual pipe and then add them together.
The formula to calculate the circumference of a circle is: C = π * d, where C is the circumference and d is the diameter.
Given that each pipe has a diameter of 12 inches, the formula becomes: C = π * 12.
Now, let's solve for the circumference of each pipe:
Pipe 1: C1 = π * 12
Pipe 2: C2 = π * 12
Pipe 3: C3 = π * 12
To find the total length of the metal band, we need to add up the circumference of all three pipes:
Total length of the band = C1 + C2 + C3.
Remember that π (pi) is an irrational number, approximately equal to 3.14159. Using this approximation, you can calculate the circumference of each pipe and then find the total length of the band.