A piece of string is wound tightly around a cylinder for 20 complete turns. The length of the string is found to be 3.96cm. calculate the diameter of the cylinder in cm
1 turn would be 3.96/20 cm = .195 cm
so πd = .195 , where d is the diameter
d = .195/π = ...
wow, that's some tiny cylinder
6.3
Why did the string go all the way around the cylinder 20 times? Because it wanted to make a fashion statement - it's all about accessorizing, you know. Now, let's solve this riddle and find the diameter.
To start, we need to find the circumference of the cylinder using the formula C = πd, where C is the circumference and d is the diameter. Since the string went around the cylinder 20 times, the total length of the string is equal to 20 times the circumference.
So we have: 20C = 3.96 cm
To find the diameter, isolate it in the formula. Divide both sides of the equation by 20: C = 3.96 cm / 20.
Now we substitute C in the formula for the circumference with the formula πd: πd = 3.96 cm / 20.
Finally, divide both sides of the equation by π: d = (3.96 cm / 20) / π.
Calculating that gives us... *drumroll* ...the diameter of the cylinder is approximately **0.063 cm**. Now that's a slim cylinder!
To calculate the diameter of the cylinder, we can use the formula for the circumference of a circle, which is given by:
Circumference = 2πr
where π is a constant approximately equal to 3.14159 and r is the radius of the circle.
In this case, we are given that the string is wound tightly around the cylinder for 20 complete turns, and the length of the string is 3.96 cm. Since each turn of the string covers the circumference of the cylinder, the total length of the string is equal to the circumference multiplied by the number of turns. Therefore, we can set up the equation:
Length of string = Circumference × Number of turns
3.96 cm = 2πr × 20
Simplifying the equation:
3.96 cm = 40πr
Dividing both sides of the equation by 40π gives:
r = 3.96 cm / (40π)
r ≈ 0.0315 cm
Finally, we can calculate the diameter of the cylinder by multiplying the radius by 2:
Diameter = 2 × r
Diameter ≈ 2 × 0.0315 cm
Diameter ≈ 0.063 cm
Therefore, the diameter of the cylinder is approximately 0.063 cm.
To solve this problem, we need to use the formula for the circumference of the cylinder. The formula is:
Circumference = 2 * π * r,
where π is a mathematical constant approximately equal to 3.14, and r is the radius of the cylinder.
However, we are given the number of turns of the string, not the circumference. So we need to convert the number of turns into the length of the string.
Since the string makes 20 complete turns around the cylinder, the length of the string is equal to the circumference of the cylinder multiplied by 20.
Therefore, the formula for the length of the string is:
Length = 20 * Circumference.
We are given that the length of the string is 3.96 cm. So we can rewrite the formula as:
3.96 = 20 * Circumference.
Now we can solve for the circumference:
Circumference = 3.96 / 20.
Circumference ≈ 0.198 cm.
Since the circumference is equal to 2 * π * r, we can now solve for the radius:
0.198 = 2 * 3.14 * r.
Divide both sides by 2 * 3.14:
r ≈ 0.198 / (2 * 3.14).
r ≈ 0.0315 cm.
Finally, to find the diameter, we can double the radius:
Diameter ≈ 2 * 0.0315.
Diameter ≈ 0.063 cm.
Therefore, the diameter of the cylinder is approximately 0.063 cm.