Difference between prism and cylinder with formulas and examples
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 Differences and Key Concepts
1. What is the difference between a prism and a cylinder?
The main difference between a prism and a cylinder is that a prism has flat polygonal bases while a cylinder has circular bases.
- A prism has two parallel, congruent polygon bases (like triangle, rectangle, pentagon).
- A cylinder has two parallel, congruent circular bases.
- Prisms have flat rectangular lateral faces, while cylinders have one curved surface.
- Both are 3D solids with uniform cross-sections.
2. What is a prism in geometry?
A prism is a three-dimensional solid with two parallel, congruent polygonal bases connected by rectangular faces.
- The bases can be triangles, rectangles, pentagons, etc.
- The shape of the base names the prism (e.g., triangular prism, rectangular prism).
- All cross-sections parallel to the base are identical.
3. What is a cylinder in geometry?
A cylinder is a three-dimensional solid with two parallel, congruent circular bases connected by a curved surface.
- The line joining the centers of the bases is the height.
- It has no vertices and no edges in the traditional sense.
- All cross-sections parallel to the base are circles.
4. What is the formula for the volume of a prism and a cylinder?
The volume of both a prism and a cylinder is calculated using Volume = Base Area × Height.
- Prism: V = B × h (where B = area of polygon base)
- Cylinder: V = πr²h (since base area = πr²)
- Both formulas show that volume depends on base area and perpendicular height.
5. How do you find the surface area of a prism and a cylinder?
The surface area equals the sum of the areas of all faces (or curved surface and bases).
- Prism: Surface Area = 2B + Ph (where B = base area, P = perimeter of base)
- Cylinder: Surface Area = 2πr² + 2πrh
- The term 2πrh represents the curved surface area of a cylinder.
6. Is a cylinder a type of prism?
A cylinder is not technically a prism, but it is often considered a similar solid because both have uniform cross-sections.
- A prism has flat polygonal faces.
- A cylinder has a curved lateral surface.
- In advanced geometry, a cylinder can be viewed as a prism with infinitely many sides.
7. What are the similarities between a prism and a cylinder?
Both a prism and a cylinder are 3D solids with parallel congruent bases and constant cross-sections.
- Both have uniform cross-sections along the height.
- Both use the formula Volume = Base Area × Height.
- Both are classified as solids with two parallel bases.
8. Can you give an example comparing the volume of a prism and a cylinder?
Yes, if both have the same base area and height, they will have the same volume.
- Example: A prism with base area 20 cm² and height 5 cm → V = 20 × 5 = 100 cm³.
- A cylinder with base area 20 cm² and height 5 cm → V = 20 × 5 = 100 cm³.
- This shows both follow the same volume principle.
9. How many faces, edges, and vertices does a prism and a cylinder have?
A prism has flat faces, edges, and vertices, while a cylinder has curved surfaces and no vertices.
- Triangular prism: 5 faces, 9 edges, 6 vertices.
- Rectangular prism: 6 faces, 12 edges, 8 vertices.
- Cylinder: 3 surfaces (2 circular + 1 curved), 2 circular edges, 0 vertices.
10. What are real-life examples of prisms and cylinders?
Common real-life examples help distinguish prisms from cylinders based on their base shapes.
- Prism examples: brick (rectangular prism), Toblerone box (triangular prism).
- Cylinder examples: soda can, water pipe, candle.
- Objects with polygon bases are prisms, while objects with circular bases are cylinders.
