Math

QuestionWhich statement about cylinders is false? A. Circular bases like prisms B. Surface includes bases and lateral C. Right cylinder axis perpendicular D. No vertex E. Oblique cylinder altitude equals axis.

Studdy Solution

STEP 1

Assumptions1. A cylinder is a three-dimensional geometric shape with two parallel circular bases and a curved surface connecting the bases. . The axis of a cylinder is the line segment connecting the centers of the two bases.
3. The altitude of a cylinder is the perpendicular distance between the two bases.
4. A right cylinder is a cylinder where the axis is perpendicular to the bases.
5. An oblique cylinder is a cylinder where the axis is not perpendicular to the bases.
6. A vertex is a point where two or more lines or edges meet.

STEP 2

Let's analyze each statement one by one.
Statement A "A cylinder is a lot like a prism, except that it has circular bases."
This statement is true. A cylinder is similar to a prism in that it has two parallel bases and a lateral surface. The main difference is that a cylinder has circular bases, while a prism can have bases of any polygonal shape.

STEP 3

Statement B "The surface of a cylinder consists of the two bases plus the lateral surface."
This statement is also true. The surface of a cylinder is made up of two parts the two circular bases and the curved lateral surface that connects the bases.

STEP 4

Statement C "A right cylinder has an axis that is perpendicular to the circular bases."
This statement is true as well. In a right cylinder, the axis, which is the line segment connecting the centers of the two bases, is indeed perpendicular to the bases.

STEP 5

Statement D "A cylinder does not have a vertex."
This statement is true. A vertex is a point where two or more lines or edges meet. Since a cylinder has a curved surface and no edges, it does not have a vertex.

STEP 6

Statement "For an oblique cylinder, the altitude is the same as the axis."
This statement is false. In an oblique cylinder, the axis (the line segment connecting the centers of the two bases) is not perpendicular to the bases, so it is not the same as the altitude (the perpendicular distance between the two bases).
The false statement is "For an oblique cylinder, the altitude is the same as the axis."

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