Table of Contents
Cross Section of a Cylinder
A cross-section of a three dimensional shape is the plane section that is perpendicular to the line of symmetries of the shape.
Generally, we come across two types of cross sections:
- Horizontal cross section
- Vertical cross section
- Horizontal cross-section: Horizontal cross-sections of a solid figure are created by crossing planes parallel to its base.
- Vertical cross-section: Vertical cross-sections of a solid figure are created by crossing planes that are perpendicular to its base.
The slicing of a solid shape determines the shape we obtain.
The image describes how a cylinder is sliced both vertically and horizontally. A horizontal cross-section results in a circle and a vertical cross-section results in a rectangle.
Rapid Recall
- A circular cross-section results from slicing a cylinder horizontally.
- A rectangular cross section results from vertically slicing a cylinder.
Solved Examples
Example 1: The water tank in the image is cylindrical and is 90 centimeters in diameter and 150 centimeters in height. Calculate the curved surface area and the surface area of this cylindrical tank.
Solution:
Height of the cylinder, (h) = 150 cm
Diameter of the tank (d) = 90 cm
Therefore, the radius of the base (r) \(\frac{90}{2}=45~cm\)
Curved surface area of the cylindrical water tank:
\(S=2\pi~rh\) [Write the formula]
\(=2\times~\frac{22}{7}\times~45\times~150\) [Substitute the values]
\( \approx 42428.57 ~cm^2\) [Multiply]
Therefore, the curved surface area of the cylindrical water tank is approximately 42428.57 square centimeters.
Total surface area of the cylindrical water jar
\(S=2\pi~r(h~+~r)\) [Write the formula]
\(= ~\left [ 2\times~\frac{22}{7}\times~45(150~+~45) \right ]\) [Substitute the values]
\( \approx ~55157.14 ~cm^2\) [Multiply]
Thereby, the total surface area of the cylindrical tank is 55157.14 square centimeters.
Example 2: What cross sections are produced when a circular pipe is cut horizontally and vertically with reference to its base?
Solution: When a circular pipe is cut, the cross section that results is:
A vertical cut: A rectangular shaped cross section is obtained, which has length equal to length of the pipe.
A horizontal cut: A circular shaped cross-section is obtained, which has a radius equal to the radius of the pipe.
Slicing a solid shape vertically or horizontally and examining the cross-sections thus obtained of the solid are two techniques to observe the various sections of a solid.
The net of a three-dimensional solid object is made up of the outlines of the faces of a specific solid object. This net when folded together creates a solid shape. A net represents the unfolded form of a solid object.
The region that results from making a plane slice across an object is known as its cross-section. This cross-section could be a rectangle, a circle, an oval, or any other flat shape depending on how the solid is sliced.