Question

Vertical cross-section of a right circular cylinder is always a :

• A. Square
• B. Rectangle
• C. Rhombus
• D. Trapezium

Hint:

To visualize cross-sections, imagine slicing through the 3D object with a flat knife. A 'vertical' cross-section usually implies a slice parallel to the height or axis of the object. For a right circular cylinder, such a slice will always produce a rectangle.

Answer 1

The Correct Option is B

Step 1: Understand what a right circular cylinder is.
A right circular cylinder is a 3D geometric shape with two parallel circular bases of the same radius and a curved surface connecting them. The axis connecting the centers of the circular bases is perpendicular to the bases. Step 2: Understand what a vertical cross-section means.
A vertical cross-section is obtained by cutting the cylinder with a plane that passes through its axis or is parallel to its axis. Step 3: Visualize the cross-section.
Imagine cutting a cylinder straight down from top to bottom. If you cut a right circular cylinder vertically, the resulting 2D shape will have two sides that are part of the curved surface (which appear as straight lines when cut vertically) and two sides that are parts of the circular bases. Let the radius of the cylinder be $r$ and its height be $h$.
When you make a vertical cut:
If the cut passes through the center of the circular bases (i.e., along the diameter), the width of the cross-section will be $2r$ (the diameter), and the height will be $h$.
If the cut is parallel to the axis but not through the center, the width of the cross-section will be less than $2r$, but the height will still be $h$.
In both cases, the opposite sides will be parallel, and all angles will be right angles (90 degrees) because the vertical cut is perpendicular to the circular bases. Step 4: Determine the shape.
A quadrilateral with all angles equal to 90 degrees is a rectangle.
While a square is a special type of rectangle (where all sides are equal), a vertical cross-section of a cylinder is not \textit{always} a square. It would only be a square if the diameter of the cylinder ($2r$) happened to be equal to its height ($h$), which is not a general property.
Therefore, the most general and always true description for a vertical cross-section of a right circular cylinder is a rectangle. Step 5: Compare with the given options.
The calculated shape is a rectangle, which matches option (2). (2) Rectangle