a cylinder is formed by first tapping together the opposite edges of a rectangular piece of paper that is 11 inches long and 8.5 inches wide. if the height of the completed cylinder 8.5 what is its volume?use 3.14 for pie
First find the diameter.
Circumference = pi * d
11 = 3.14d
11/3.14 = d
3.5 = d
So the radius = 1.75
Then use this formula for the volume of a cylinder.
V = pi * r^2 * h
http://www.mathsteacher.com.au/year9/ch14_measurement/18_cylinder/cylinder.htm
i am sorry ms. sue i still don't get it could you please give me an explanation for 'dummies' thank you
The circumference is formed by the 11" piece of paper.
We need to find the diameter.
Circumference = pi * d
11 = 3.14d
11/3.14 = d
3.5 = d
The radius is half the diameter -- 1.75
Now we can use the formula for volume.
V = pi * r^2 * h
V = 3.14 * 1.75^2 * 8.5
V = 3.14 * 3.1 * 8.5
Now multiply those three numbers to find the volume.
Also see the website I posted.
Maybe you don't get it because you confused "tapping" in your question with "taping".
The ends are taped together. The 11 inch width of the paper becomes the circumference of the circular base area of the cylinder.
What don't you understand in MsSue's explanation? Multiply the last three numbers in her answer to get the volume.
To find the volume of a cylinder, you need to use the formula: Volume = π * radius^2 * height.
In this case, the height of the completed cylinder is provided as 8.5 inches. However, we still need to calculate the radius.
When you tap together the opposite edges of the rectangular paper, you will form the circumference of the base of the cylinder. The length of the paper becomes the circumference, and we can use the formula for circumference to find the radius.
The formula to find the circumference (C) of a circle is: C = 2 * π * r, where r represents the radius.
Given that the length of the paper is 11 inches, we can set up the equation to find the circumference:
11 = 2 * π * r
Now, we can solve for r:
r = 11 / (2 * π)
r ≈ 1.75 (rounded to two decimal places)
Now that we have the radius (approximately 1.75 inches) and the height (8.5 inches), we can calculate the volume:
Volume = π * (1.75^2) * 8.5
Volume ≈ 65.95 cubic inches (rounded to two decimal places)
Therefore, the volume of the cylinder is approximately 65.95 cubic inches.