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.
(Image will be uploaded soon)
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 the main difference between a prism and a cylinder?
The main difference lies in their bases and lateral surfaces. A prism has two identical, parallel polygonal bases (like triangles or squares) and its lateral faces are flat parallelograms. In contrast, a cylinder has two identical, parallel circular bases and a single curved lateral surface.
2. What defines a 3D shape as a prism?
A prism is a three-dimensional solid, or polyhedron, defined by two key features:
- It has two identical and parallel faces called bases. These bases are polygons (e.g., triangles, squares, pentagons).
- Its other faces, called lateral faces, are parallelograms that connect the corresponding sides of the bases.
3. What are the defining characteristics of a cylinder?
A cylinder is a three-dimensional solid shape characterized by:
- Two identical, parallel, and flat circular ends, which are its bases.
- A single, continuous curved lateral surface that connects the circular bases.
4. Can a cylinder be considered a special type of prism?
Conceptually, yes. You can think of a cylinder as a prism where the base polygon has an infinite number of sides. As you keep increasing the number of sides of a regular polygon (e.g., from a hexagon to an octagon, and so on), the shape of the base gets closer and closer to a circle. Therefore, a cylinder can be seen as the theoretical limit of a prism with a regular polygonal base as the number of sides approaches infinity.
5. How do the formulas for calculating the volume of a prism and a cylinder relate to each other?
The volume formulas for both shapes follow the same fundamental principle: Volume = Area of the Base × Height.
- For a prism, the volume is V = (Area of the polygonal base) × h.
- For a cylinder, the volume is V = (Area of the circular base) × h, which simplifies to V = πr²h.
6. Why is it important to distinguish between prisms and cylinders in real-world applications?
Distinguishing between them is crucial for design, manufacturing, and packaging. For example:
- Prisms, like cardboard boxes (rectangular prisms) or Toblerone packages (triangular prisms), are chosen for their flat faces, which make them easy to stack and pack efficiently.
- Cylinders, like cans, pipes, or pillars, are often used when pressure needs to be distributed evenly (like in a soda can) or when a smooth, rolling motion is required. Their curved surface makes them structurally strong against internal pressure but less space-efficient for packing compared to prisms.
7. Are all prisms triangular? Explain with examples.
No, not all prisms are triangular. The type of prism is determined by the shape of its polygonal base. For example:
- A triangular prism has triangular bases.
- A rectangular prism (like a cuboid) has rectangular bases.
- A square prism has square bases.
- A pentagonal prism has pentagonal bases.
8. What is a common mistake students make when identifying the base of a prism?
A common mistake is identifying the wrong face as the base, especially with rectangular prisms. Students might assume the face the prism is resting on is its base. However, the bases of a prism are the two parallel and congruent polygonal faces. For a triangular prism, the bases are always the two triangles, even if the prism is lying on one of its rectangular lateral faces. Correctly identifying the base is essential for calculating volume and surface area accurately.
