cylindrical can is to be made from a rectangular piece of aluminum that is 25 inches long and 10inches high by rolling the metal horizontally. Determine the circumference of the cylinder, the radius of the cylinder, the height of the cylinder, and the volume of the cylinder
C=25 that is given, height is 10
So what is the question?
To determine the circumference of the cylinder, we need to find the length of the rectangular piece of aluminum that will become the circumference of the cylinder when rolled.
The circumference of a cylinder is equal to the perimeter of its base, which in this case is the rectangular piece of aluminum. The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
In this case, the length of the rectangular piece is 25 inches, and the width (which will become the circumference when rolled) is 10 inches. Therefore, the circumference of the cylinder is:
Circumference = 2 * (25 + 10)
Circumference = 2 * 35
Circumference = 70 inches
So, the circumference of the cylinder is 70 inches.
To determine the radius of the cylinder, we can use the formula:
Radius = Circumference / (2 * π)
Since we already calculated the circumference as 70 inches, we can substitute this value into the formula:
Radius = 70 / (2 * π)
Radius = 35 / π
Radius ≈ 11.14 inches (rounding to the nearest hundredth)
So, the radius of the cylinder is approximately 11.14 inches.
The height of the cylinder is the same as the height of the original rectangular piece, which is given as 10 inches.
Therefore, the height of the cylinder is 10 inches.
To calculate the volume of the cylinder, we can use the formula:
Volume = π * (Radius^2) * Height
Substituting the values we have:
Volume = π * (11.14^2) * 10
Volume ≈ 3892.12 cubic inches (rounding to the nearest hundredth)
So, the volume of the cylinder is approximately 3892.12 cubic inches.