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If you cut a watermelon by its middle, then the upper red surface will be its cross section, you can also see in the given figures (Example of cross section).
So, these are some examples of the cross-section. I hope your understanding is getting clear about this topic after seeing the pictures.
Now we are going to learn about the cross section of any object, and it is good to know that area of cross section helps us in finding solutions of many the problems.
Types Of Cross Section
There are two types of the cross-section.
The first one is Horizontal Cross Section (also known as Parallel Cross Section).
And, second is Vertical Cross-Section (also known as Perpendicular Cross Section).
Let’s know something about both types in detail-
Horizontal Cross Section and also known as Parallel Cross Section
When we cut any of the surfaces horizontally which is parallel to its base, then created a cross section is known as Horizontal Cross Section.
Vertical Cross Section and also known as Perpendicular Cross Section
When we cut any of the surfaces vertically, which is perpendicular to its base, the generated cross section is Vertical Cross Section.
Cross Section in geometrical Shapes
You must have seen different geometrical shapes in your studies and in daily life as well. We can also create cross section in these Geometrical 3D shapes. You have come across with a new term that is 3D Shapes, like Sphere, Cuboid, Cube, etc.
You can create cross sections in 3D figures only, not in 2D shapes.
Area Of Cross section
When you cut a solid 3D shape, then the obtained figure will also have an area of cross section.
Volume of Cross section
When you create the cross section of any figure, you must have notice that, obtained cross section is 2D dimension. And you know that we cannot find volume of a 2D figure.
Cross section of a cylinder
Cylinder has different types of cross sections. It may be rectangle, circle or oval, depends only upon how you will cut it.
If you cut the cylinder horizontally, then the obtained cross section is circular.
But if you cut it vertically that is perpendicular to base, then the obtained cross section is rectangular.
And, if you cut the cylinder horizontally but with slight different angle, then the shape created will be oval.
Hope, you will understand it better after seeing the following Picture
Cross Section Of different Shapes
Cross Section of sphere
On creating cross sections in a sphere, then you will see that every figure is Circular.
Cross Section of Cone
Case of cone is very interesting, you can get cross sections of different shapes, as discussed earlier, the method of cutting decides the shape of cross section of cone.
Cross Section Diagram of Kidney
Here, You will see the cross section diagram of the kidney. Actually, it is for telling you that you can create cross sections of any solid shape. The cross-section of the kidney with brief naming of each part has been mentioned below-
Solved Example-
Find the cross section area of the cylinder when it is cuts horizontally with base, if radius of base is 7 cm and height of cylinder is 10 cm.
Sol. We know that, cylinder’s horizontal cross section is circular, then the area of cross section will be the area of that circle.
A = πr2
⇒ r = 7 cm
⇒ A = (7)2
A = 227 × 7 × 7
A = 22 × 7
A = 154 cm2
Hence, area of cross section of the cylinder is 154 cm.
A sphere having radius 14 cm is cuts across its diameter. Find out its area of cross section.
Sol: As, we know that we are talking about sphere, so every cross section is circular. And, as we are finding area about diameter so radius of the circular cross section is same as radius of sphere.
A = πr2
⇒ r = 14 cm
⇒ A = (14)2
A = 227 × 14 × 14
A = 22 × 2 × 14
A = 616 cm2
Conclusion
We have learned about a cross-section of three-dimensional figures. We have even learned the method to find areas of the cross-section with some of the examples. The main and common use of cross-section is to find the area of the cross-section of any of the figures. We have talked in detail about the types of cross-sections which are horizontal cross-sections and vertical cross-sections. The cross-section of different shapes has also been discussed which includes a cross-section of a sphere, cone, and even a detailed explanation of the cross-section of a kidney.
