Prism Vs Cylinder

Dhristi JEE 2022-24

What is 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.

Types of Prism

Depending on the basis of the type of polygon base, the prisms are classified into two types:

  • Regular prism: The prism is a regular prism if the base of the prism is in the shape of a regular polygon.

  • Irregular prism:  An irregular prism is a prism in which the base is in the shape of an irregular polygon.

Based on the shape of the bases, it is further categorized into different types:

Triangular prism: A triangular prism is a prism whose bases are triangular in shape.


Rectangular prism: A prism whose bases are rectangular in shape is considered a rectangular prism (a rectangular prism is cuboidal in shape).


Apart from regular and irregular, the prism is often classified into two different types based on the alignment of the bases:

  • Right Prism: The two flat ends that are perfectly aligned with all the side faces in the shape of a rectangle is a right prism.


  • Oblique prism: This prism appears to be titled and sides faces are parallelograms and the two flat ends are not aligned.


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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

A cylinder is a prism with only one account 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 that can be cast on a screen.


Having observed the characteristics of a cylinder, we can say that a cylinder is a prism with countless 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 of circular cylinder


​= (Area of circle). (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

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 the 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


= 600 cm2

Example:

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

Solution:


Using the formula for Surface Area = 2b + ph


2(600cm2) + 140 cm (5)


= 1200 cm2 + 700


= 1900 cm2

Example: 


The apothem length of a hexagon angle along with its prism base length and the height are given as 7 cm, 11 cm, and 16 cm, respectively. Find the total surface area.


Solution:


Total surface area formula of hexagonal prism:


TSA = 6ab + 6bh


Substituting the values we get,


TSA = 6 × 7 × 11 + 6 × 11 × 16


= 462 + 1056


= 1518 cm2

FAQs on Prism Vs Cylinder

1. What is a Cylinder?

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

2. What is a Prism?

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.

3. Why do we calculate the surface area of a Prism?

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.

4. How is a cylinder similar to a prism?

A prism is a solid with sides as flat surfaces and bases that are polygons. Imagine a prism with regular polygons for bases; now as you increase the number of sides, the solid looks just like a cylinder. So, we can thus say that a cylinder is a prism with an infinite number of faces. There is also a similarity between cylinder and prism as a cylinder has the same cross-section anywhere, its volume is calculated by multiplying the height by the area of the base. It can be oblique or right.

5. How is a cylinder different from a prism?

The difference between a cylinder and a prism is that a cylinder is basically a tube that is composed of a rectangle whose base is the circumference of the circle and two parallel congruent circles whereas a prism is a solid figure that has two parallel congruent sides known as the bases which are connected by the lateral faces that are parallelograms.

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