A length 550cm of tin thread wraps around a cylinder exactly 25times. Calculate the circumference and the radius of the cylinder.
25 times the circumference = 550 cm
so 1 circumf = 550/25 = 22 cm
circumf = 2πr
2πr = 22
r = 11/(π) = ..... cm
To calculate the circumference and radius of the cylinder, we need to use the formula for the circumference of a cylinder.
The formula for the circumference of a cylinder is:
C = 2πr
Where C is the circumference and r is the radius.
In this case, we know that the length of the tin thread wraps around the cylinder exactly 25 times, which means it represents the circumference of the cylinder.
So, we can write the equation as:
550 cm = 25 * C
To calculate C, we divide both sides of the equation by 25:
C = 550 cm / 25
Now, we can substitute the value of C into the formula for the circumference:
C = 22 cm
Therefore, the circumference of the cylinder is 22 cm.
To find the radius, we can rearrange the formula for the circumference:
C = 2πr
Simplifying the equation, we have:
22 cm = 2πr
Dividing both sides of the equation by 2π, we get:
r = 22 cm / (2π)
Now, we can calculate the value of r using a calculator:
r ≈ 3.5 cm
Therefore, the radius of the cylinder is approximately 3.5 cm.
To find the circumference and radius of the cylinder, we need to use the formula:
Circumference = 2πr
Given that the tin thread wraps around the cylinder 25 times, we can set up the equation:
25 * Circumference = 550 cm
Simplifying the equation, we get:
Circumference = 550 cm / 25
Circumference = 22 cm
Now we can use the circumference formula to find the radius:
Circumference = 2πr
Substituting the known circumference value, we have:
22 cm = 2πr
Dividing both sides of the equation by 2π, we get:
11 cm/π = r
So the radius of the cylinder is approximately 3.5 cm (rounded to one decimal place).