A square prism is usually a cuboid, that has actually square bases. The has four rectangular faces and two square-shaped ends. In Geometry, we have studied miscellaneous three-dimensional forms called solid shapes or solids. Some examples are cubes, cuboids, cylinders, prisms, spheres, hemispheres, and so on.
You are watching: How do you find the volume of a square prism
A square prism is another type of 3d shape that is a cuboid, v its two-end encounters square in shape. An amazing fact is, all the cubes are square prisms, however not all the square prisms are cubes. It is since the lateral encounters of the square prism can be rectangle-shaped or square.
In this article, we space going to emphasis on the square prism definition, types, surface ar area, and volume formulas, net and examples.
|Table the contents:Types of square prismFormulas that square prism|
Square prism Definition
A square prism is a three-dimensional form cuboid figure whose bases are squares and the other four deals with are rectangle in shape. The contrary sides and angles space congruent to each other. An example of a shape of a square prism is a magnet bar.
In the provided figure, the bases the the prism are square and also lateral deals with are rectangular, and also therefore, it is referred to as a square prism.
Properties of Square prism
A square prism has 4 rectangular faces between two square faces. Some essential properties that the square prism are:A square prism has actually 6 faces, 12 edges and also 8 verticesOpposite sides of square prisms space parallel to every otherOpposite sides of square prisms space congruent to every otherOpposite angle of square prisms space congruent to each otherDiagonals of square prism bisect each otherConsecutive angles of square prisms space supplementary
Types the Square prism
Square prisms space of 2 types. They are:Right Square PrismOblique Square Prism
Right Square Prism
A prism with square bases is referred to as a square prism. If the lateral faces of a square prism room perpendicular come its base, then it is described as the appropriate square prismVertices that a square prism = 8Edges of a square prism = 12Faces of a square prism= 6 (including bases)
Oblique Square Prism
If the lateral deals with (rectangular faces) the a square prism space not perpendicular to the square bases, then it is recognized as an tilt prism.
Square Prism Formulas
Since a square prism is a hard shape, hence, it has two main formulas:Surface Area the a square prismVolume that a square prism
Surface Area that a Square Prism
The surface ar area that a square prism is the measure of the full area of a surface ar of a three-dimensional solid object. The is express in square units. The surface ar area the a prism is characterized as the amount of twice the basic area and also the lateral surface area of the prism.
The surface ar area the a square prism formula is offered as:
|Surface area of the square prism, SA = 2a2 + 4ah square units|
a is the side of the square prism
h is the height of the square prism.
Volume of a Square prism
The volume that a square prism is a measure up of the populated units the the solid. The volume the a square prism is the variety of units supplied to to fill a cube. That is stood for by cubic units. The volume of a square prism formula is as follows,
The volume that a square Prism = Area of basic × height of the prism
If “a” is the side of the base, and also “h” is the height of the prism, then:
|Volume a Square Prism, V = a2 h cubic units.|
Square Prism Net
If us open and flatten, we can obtain the network of the square prism. The net of the square prism will give an exact view of 2 square faces and four rectangle-shaped faces.
Square Prism resolved Examples
Q.1: What is the surface area of a square prism whose side is 3 cm and height is 5 cm?
Side, a = 3 cm
Height, h = 5 cm
The surface area of the square prism, SA = 2a2 + 4ah square units
Now, instead of the provided values
SA = 2(3)2 + 4(3)(5) cm2
SA = 2(9) + 4(15) cm2
SA = 18 + 60 cm2
SA = 78 cm2
Therefore, the surface ar area the a square prism is 78 cm2
Q.2: What is the volume that a square prism whose next is 3 cm and also height is 5 cm?
Side, a = 3 cm
Height, h = 5 cm
The Volume a Square Prism, V = a2 h cubic units.
V = (3)2 (5)
V = 9 (5)
V = 45 cm3
Therefore, the volume the a square prism is 45 cm2.
Practice concerns on Square PrismIf the next length and height that the square prism space 5cm and also 12 cm, respectively, uncover its surface area and volume.The volume that a square prism is 160 cu.cm. What is the size of that sides, if the elevation of the square prism is 10cm?
Frequently Asked concerns – FAQs
What is a square prism?
A square prism is a prism that has its end-faces square in shape and the other four deals with are usually rectangle-shaped in shape.It a three-dimensional cuboid shape.
What is the formula for square prism?
A square prism has actually two key formulas.Surface area that a square prism = 2a2 + 4ahVolume of a square prism = a2hwhere, a side-length and h is the height of prism.
See more: What Does Coefficient Mean In Chemistry, What Is A Coefficient In Science
Are every the cubes a square prism?
Yes, all the cubes are square prisms, but not all the square prisms are cubes.