Respuesta :
Answer:
A: The height of the cylinder is 3.4 ft.
C: The diameter of the cylinder is about 3 ft.
E: A right cylinder with the same height and radius as this oblique cylinder would also have a volume of 24 ft3.
Step-by-step explanation:
The correct statement about the oblique cylinder is the height of the cylinder is 3.4 ft, while the diameter of the oblique cylinder is 3 ft.
What is the volume of an oblique cylinder?
The volume of an oblique cylinder is equal to the volume of a straight cylinder with the same radius and perpendicular height.
As it is given that the volume of the oblique cylinder is 24 ft³. Since we know that the volume of an oblique cylinder is equal to the volume of a straight cylinder with the same radius and perpendicular height. This makes the last statement one of the correct options.
As in the given options, there is only one option that states the height of the cylinder if we assume the statement to be correct, the radius of the cylinder can be written as,
[tex]\rm \text{Volume of cylinder} = \pi r^2 h\\\\24 = \pi (r)^2 \times 3.4\\\\r^2 = 2.247\\\\r = 1.4989 \approx 1.5\ feet[/tex]
Since the radius of the cylinder is 1.5 feet, the diameter will be twice the radius of the cylinder, therefore, 3 ft.
Now, if the diameter of the cylinder is assumed to be 4.5 feet, then the height of the cylinder will be,
[tex]\rm \text{Volume of cylinder} = \pi r^2 h\\\\24 = \pi (2.25)^2 \times h\\\\h=1.5 \ feet[/tex]
As we can see that when the diameter of the cylinder is kept at 4.5 feet, then the height of the cylinder must be 1.5 feet, but since this option about the height of the cylinder is not available we can validate the answer.
Thus, the statement that is correct about the oblique cylinder are:
- The height of the cylinder is 3.4 ft.
- The diameter of the cylinder is about 3 ft.
- A right cylinder with the same height and radius as this oblique cylinder would also have a volume of 24 ft³.
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