Prism Vs Cylinder

What is the Difference Between a Prism and a Cylinder?

A prism is a solid figure composed of two parallel congruent sides known as its bases joined by the lateral faces that are parallelograms. On the other hand, a cylinder is a tube consisting of two parallel congruent circles and a rectangle whose base is the circumference of the circle. Moreover, Prisms are 3-dimensional solid shapes that consist of sides and faces that are polygons – 2-dimensional shapes containing straight sides. Both prism and pyramid fall under the larger category –polyhedrons – since the sides and bases are polygons. Prisms do not have rounded sides, rounded angles, or rounded edges in contrast to cylinders and spheres.


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How a Cylinder Differentiates From a Prism

Taking into account the characteristics of prisms, this removes the cones, cylinders, and spheres as prisms since they have curved faces. This also removes pyramids since they don't contain identical base shapes or identical cross sections throughout.


Is a Cylinder a Prism

Cylinder is a prism only one accounts i.e. both are solids. Cylinders and prisms are alike on this common characteristic. That being said, let’s see what a cylinder is and how it differs from a prism.

  • A cylinder is a geometrical figure of revolution while a prism is not.

  • A cylinder consists of 2 flat ends and a curved surface while a prism contains two polygons for the two ends and the remaining are plain rectangular faces.

  • A cylinder does not have any diagonals while a prism contains many.

  • A cylinder consists of only one shape while a prism has many shapes depending on the shape of the two ends.

  • A cylinder has no vertices while a prism has various vertices.

  • A cylinder contains 2 curved edges while a prism has no curved edge

  • A cylinder has 2 circular ends while a prism can have ends that are rectangular, triangular, regular or irregular polygon or pentagon.

  • A cylinder made up of glass does not scatter white light while a glass prism creates spectrums which can be casted on a screen.

Having observed the characteristics of a cylinder, we can say that a cylinder is a prism with countless numbers of faces. This means that a prism becomes a cylinder as the number of sides of its base becomes bigger and bigger.


Circular Cylinders

When we say is a cylinder a prism, we sometimes mean a cylindrical prism. It means a circular cylinder which is a prism-like figure and has a base shaped like a circle.

Volume circular cylinder

​= (Areacircle). (Height)

= (π⋅ (radius)²)⋅(height)

= πr²h


Prisms and Prism-Like Figures

Volume of Prism = (Base Area) . (Height)

We measure the height of a prism perpendicularly with respect to the plane of its base. That's true even when a prism is on its side or when it tilts which is known as an oblique prism).


Rectangular Prisms

Time and again, we first learn about volume using rectangular prisms (particularly right rectangular prisms), such as by constructing the prism out of cubes.

Remember that any face of a rectangular prism could be its base, in as much as we measure the height of the prism perpendicularly to that face.


Solved Examples

Example:

You have a right rectangular prism and you're required to find the perimeter and area of base. The measurement of the given prism is as follows:

Length = 60 cm

Width = 10 cm

Height = 5 cm


Solution:

To calculate the perimeter, use the formula to find out the perimeter of a rectangular prism because the name tells you the base is a rectangle:

Perimeter = 2l + 2w

= 2(60) + 2(10)

=120 cm+20 cm

=140 cm

The area of the base is equivalent to length × width (as it always is for a rectangle), which is:

Area of base

= 60 cm × 10 cm

= 6002 cm


Example:

Find out the surface area of the rectangular prism of the above example?

Solution:

Using the formula for Surface Area = 2b + ph

2(600 cm2) + 140 cm (5)

= 1200 cm2 + 700

1900 cm2.


Conclusion:

With that, strictly speaking a cylinder is a prism does not make sense. However both are extremely similar.

FAQs (Frequently Asked Questions)

Q1. What is a Cylinder?

Answer: In geometrical terms, a cylinder is a solid shape encompassed by a cylinder and two parallel planes intersecting the cylinder.

Q2. What is a Prism?

Answer: A prism is a 3-dimensional solid figure that consists of the following characteristics:

  • It is a polyhedron​(stating a solid figure).

  • It is a parallelogram​(a four-sided figure with opposite sides parallel to each other).

  • The cross section ​of the figure is exactly the same throughout the length of the object.

  • It has ​flat​ faces and not curved faces.

  • The two end shapes are congruent​.

The name of the prism arises from a geometrical shape of the two ends, known as the bases. This can be any figure (except for curves or circles). For example, a prism with a square base is called a square prism. A prism with a triangular base is called a triangular prism and this list goes on.

Q3. Why do we Need to Calculate the Perimeter of a Prism?

Answer: Finding the perimeter of a prism is a crucial calculation that factors into volume and surface area formulas for some prisms. For example, the formula for finding the surface area of a right prism (a right prism has similar sides and bases that are all rectangular):


Surface Area = 2b + ph

Where, 

b ​= Area of the base,

p = The perimeter of the base

h​ = The height of the prism.