[Maths Class Notes] on Prism Vs Cylinder Pdf for Exam

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:

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:

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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