you are given one sheet of computer paper (8.5x11 inches). if you were to make two different cylinders with the paper (hot dog and hamburger style), which volume is greater?
hot dog of course
To find out which volume is greater between the hot dog style and hamburger style cylinders made from an 8.5x11 inch sheet of paper, we need to calculate the volumes of both cylinders.
First, let's understand the difference between the two styles:
1. Hot dog style: The paper is rolled up along its shorter edge, creating a cylinder with a height equal to 8.5 inches (the length of the paper) and a radius equal to 11 inches (half of the width of the paper).
2. Hamburger style: The paper is rolled up along its longer edge, creating a cylinder with a height equal to 11 inches (the width of the paper) and a radius equal to 8.5 inches (half of the length of the paper).
Now, let's calculate the volumes of each cylinder using the formula for cylinder volume:
Volume = π * r^2 * h
where π (pi) is approximately 3.14159, r is the radius, and h is the height.
For the hot dog style cylinder:
Radius = 11 inches / 2 = 5.5 inches
Height = 8.5 inches
Volume = π * (5.5 inches)^2 * 8.5 inches
For the hamburger style cylinder:
Radius = 8.5 inches / 2 = 4.25 inches
Height = 11 inches
Volume = π * (4.25 inches)^2 * 11 inches
By substituting in these values and calculating the volumes, we can determine which volume is greater.