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
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To determine the circumference, radius, height, and volume of the cylinder made from the rectangular piece of aluminum, follow the steps below:
1. Circumference of the Cylinder:
- The circumference (C) of a cylinder can be calculated using the formula C = 2πr, where r is the radius.
- The rectangular piece of aluminum will be rolled horizontally, resulting in the height becoming the circumference of the cylinder.
- Therefore, the circumference will be 10 inches.
- C = 10 inches.
2. Radius of the Cylinder:
- Since the circumference (C) is given as 10 inches, we can use the formula C = 2πr to calculate the radius (r).
- Rearrange the formula to solve for r: r = C / 2π.
- Substituting the given value of C: r = 10 / (2π).
- Calculate the value of r: r ≈ 10 / (2 × 3.14) ≈ 10 / 6.28 ≈ 1.59 inches.
- Therefore, the radius (r) of the cylinder is approximately 1.59 inches.
3. Height of the Cylinder:
- The height of the cylinder is the same as the length of the rectangular piece, which is given as 25 inches.
- Therefore, the height (h) of the cylinder is 25 inches.
4. Volume of the Cylinder:
- The volume (V) of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
- Substitute the given values of r and h into the formula: V = π(1.59)^2 × 25.
- Calculate the volume: V ≈ 3.14 × (1.59)^2 × 25 ≈ 3.14 × 2.5281 × 25 ≈ 200.0876 cubic inches.
- Therefore, the volume (V) of the cylinder is approximately 200.0876 cubic inches.
In summary:
- The circumference of the cylinder is 10 inches.
- The radius of the cylinder is approximately 1.59 inches.
- The height of the cylinder is 25 inches.
- The volume of the cylinder is approximately 200.0876 cubic inches.