A rectangular piece of card 12 cm by 20 cm
is rolled up to make atube(with no overlap)Find the radius of tube if
i) the long sides are joined
Take a sheet of printer paper and try it.
Doesn't the circumference of your tube equal the long side ?
So....
2πr = 20
r = 10/π
To find the radius of the tube when the long sides are joined, we can use the formula for the circumference of a circle:
C = 2πr
Since the long sides of the rectangular piece of card are joined to create the circumference of the circle, we can equate the length of the rectangle to the circumference of the circle:
C = 2πr (equation 1)
where C is the length of the rectangle.
The length of the rectangle is given as 20 cm, so we can substitute this value into equation 1:
20 = 2πr
Now, to find the radius (r), we can rearrange the equation:
r = 20 / (2π)
Using a standard approximation for π (3.14), we can calculate the radius:
r = 20 / (2 * 3.14)
r = 20 / 6.28
r ≈ 3.18 cm
Therefore, the radius of the tube when the long sides are joined is approximately 3.18 cm.
To find the radius of the tube when the long sides of the card are joined, we need to use the formula for the circumference of a circle.
The circumference of a circle is given by the formula: C = 2πr, where C represents the circumference and r represents the radius of the circle.
In this case, when the long sides of the card are joined, the circumference of the tube will be equal to the length of the card, which is 20 cm.
So we have the equation:
20 = 2πr
To find the radius, we can rearrange the equation as follows:
r = 20 / (2π)
Now, we can use a calculator to calculate the value of r:
r ≈ 20 / (2 × 3.14159) ≈ 20 / 6.28318 ≈ 3.1831 cm
Therefore, the radius of the tube, when the long sides of the card are joined, is approximately 3.1831 cm.