Three cylindrical tubes with with a 12 in diameter are strapped together by a plastic band. How long is the band?Suppose that four of the same tubes are strapped together with a snugly fitting plastic band how long is the band?
1st part:
Visualize three identical coins touching each other to form a "triangle". What is the circumference.
(actually make the sketch using 3 quarters)
Join the centres, you will get an equilateral triangle with sides 12.
Your circumference around the outside consists of 3 straight sections, each equal to 12, plus 3 arc-lengths each equal to 1/3 of the circle circumference
so it looks like the length of the band
= 3(12) + circumference of one circle
= 36 + 12π
Now take 4 coins. If you start with a "square" arrangement, I thing the plastic band will squish them and you will have another coin tucked into one of the corners above
Do a similar analysis as before.
To find the length of the plastic band, we need to calculate the circumference of a single tube and then multiply it by the number of tubes.
For a single tube with a 12-inch diameter, we can use the formula for the circumference of a circle:
Circumference = π * diameter
Given that the diameter is 12 inches, we can substitute it into the formula:
Circumference = π * 12 inches
Calculating the value:
Circumference = 3.14 * 12 inches
Circumference = 37.68 inches
So, the circumference of a single tube is 37.68 inches.
Now, let's calculate the length of the plastic band when three cylindrical tubes are strapped together:
Length of the band = Circumference of a single tube * Number of tubes
Length of the band = 37.68 inches * 3
Length of the band = 113.04 inches
Therefore, when three cylindrical tubes with a 12-inch diameter are strapped together, the length of the plastic band is 113.04 inches.
For the second part of the question, let's calculate the length of the plastic band when four tubes are strapped together:
Length of the band = Circumference of a single tube * Number of tubes
Length of the band = 37.68 inches * 4
Length of the band = 150.72 inches
So, when four cylindrical tubes with a 12-inch diameter are strapped together, the length of the plastic band is 150.72 inches.
To find the length of the plastic band in the first scenario, where three cylindrical tubes with a 12-inch diameter are strapped together, we need to calculate the circumference of each tube and add them together.
Step 1: Calculate the circumference of one tube:
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 the diameter of each tube is 12 inches, the circumference can be calculated as follows:
C1 = π * 12
Step 2: Calculate the total length of the plastic band for three tubes:
Since we have three tubes, we need to multiply the circumference of one tube by 3.
Total length = 3 * C1
Now, let's calculate the total length of the plastic band for three tubes:
Total length = 3 * (π * 12)
In the second scenario, where four of the same tubes are strapped together with a snugly fitting plastic band, the process would be similar.
Step 3: Calculate the total length of the plastic band for four tubes:
Total length = 4 * C1
Now, let's calculate the total length of the plastic band for four tubes:
Total length = 4 * (π * 12)
This will give us the length of the plastic band in each scenario.