Question

What is the vertical cross-section of a solid cylindrical pipe shown in the figure?

(a) An ellipse
(b) A circle
(c) A cylinder
(d) A rectangle

Answer 1

Hint: We must assume a vertical plane cutting through the solid cylinder. We will need to visualize and by proper analysis, we can say that the cross section of the cut-out will be a rectangle. We can also try to eliminate all other options to get to the correct answer.

Complete step by step answer:
We have the given figure which represents a solid cylinder.

We need to find the vertical cross section of this cylinder.
We must understand here, that the vertical cross section is the figure formed by cutting the solid cylinder vertically.
On doing so, we will get the following figure.

By carefully examining the above figure, we can see that the cross section has a shape of rectangle.
Hence, option (d) is the correct answer.
We know that the cross section of any three dimensional object is a two dimensional shape. Hence, it is clear that the cross section of a cylinder can never be a cylinder, because a cylinder is a three dimensional object. So, option (c) can never be our answer.
If we think about the cross section at a finite angle, less than right angle, from the vertical, then we can get either an ellipse or a rectangle as the cross section. We have shown the formation of ellipse in the figure below,

But, in this problem, we are concerned with the vertical cross section, so option (a) is also not an answer.
If we consider the horizontal cross section of this solid cylinder, we will get a circle. The formation of circular cross section is shown in figure below,

But, in this problem, we are concerned about the vertical cross section. Thus, option (b) is also not an answer to this problem.
Thus, from the above analysis, and elimination of all other options, we can say that the rectangle is the vertical cross section of this solid cylinder.

So, the correct answer is “Option d”.

Note: This problem needs some vivid imagination. We must take time and think of all the possibilities that may arise. We must understand that the vertical cross section means the shape of the cut-out after being cut by a vertical plane.