MathsVolume of a Prism

Volume of a Prism

Volume of Prism Formula

Volume of a Prism.

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    The volume of a prism is the product of the area of the base and the height of the prism. The volume of a prism is given by the formula:

    Volume = (area of base) × (height)

    Volume of a Prism

    What is Prism?

    A three-dimensional solid shape having its base and top as identical polygons and side faces as parallelograms are called a prism.

    A Prism is a Solid Object with:

    • Identical base and top which are parallel to each other.
    • The side faces are flat and parallelogram
    • No curve sides
    • And the same cross-section along with its length.

    Different Types of Prism

    A prism is a solid three-dimensional geometric figure with two similar ends and all flat sides. The prism is named after the shape of its base, hence a prism with a triangular base is called a “triangular prism”. So the different types of prisms are given their names on the basis of their cross-sectional figure formed.

    Types of Prisms are:

    • Triangular Prism
    • Square Prism
    • Cube
    • Cuboid or rectangular Prism
    • Pentagonal Prism

    What is Volume of a Prism?

    As the prism is a 3D solid object it has both the surface area and volume.

    The volume of a 3D prism is defined as the total space occupied by that object.

    To calculate the volume of a prism, you just have to calculate the area of its base and multiply it by its height.

    (image will be uploaded soon)

    Therefore Volume General Formula it is Represented as,

    Volume of a Prism (V) = Base Area × Length

    The volume of a three-dimensional prism is represented as cubic units.

    Here’s how to calculate the volume of a variety of prisms.

    Volume of Prism Formula

    Different prisms have different volumes. So the formula to calculate the volume of different Prisms are:

    • Triangular Prism

    A prism having its base and top as identical triangles and the lateral faces are rectangles is called a triangular prism.

    A triangular prism has

    • 5 faces
    • 6 vertices and
    • 9 edges

    (image will be uploaded soon)

    Volume of Triangular Prism = (

    1212

    ) a x b x h

    Where,

    a = Apothem length of a triangular prism

    b = Base length of a triangular prism

    h = height of a triangular prism

    • Square Prism

    In a square prism, the base and top are congruent squares and the lateral faces are rectangles

    A square prism has

    • 6 faces
    • 8 vertices and
    • 12 edges

    (image will be uploaded soon)

    Volume of a Square Prism = l x b x h

    Where

    l = length of a square prism

    b = Base of a square prism

    h = height of a square prism

    • Cube

    If a square prism has all of its faces as identical squares, then it is called a cube prism.

    A cubic prism or a cube has

    • 6 faces
    • 8 vertices and
    • 12 edges

    (image will be uploaded soon)

    Volume of a Cube Prism =

    a3a3

    Where

    a = edges of a cube prism( because l = w = h = a)

    • Cuboid or Rectangular Prism

    If the base and top of the prism are identical rectangles, then it is a rectangular prism or a cuboid.

    A cuboid prism has

    • 6 faces
    • 8 vertices and
    • 12 edges

    (image will be uploaded soon)

    Volume of Rectangular Prism = l x b x h

    Where

    l = length of a rectangular prism

    b = Base of a rectangular prism

    h = height of a rectangular prism

    • Pentagonal Prism

    If the base and top of a prism are pentagons, then it is called a pentagonal prism.

    A pentagonal prism has

    • 7 faces
    • 10 vertices and
    • 15 edges

    (image will be uploaded soon)

    Volume of Pentagonal Prism = (

    5252

    ) a x b x h

    Where,

    a – Apothem length of the pentagonal prism.

    b – Base length of the pentagonal prism.

    h – Height of the pentagonal prism

    • Hexagonal Prism

    A hexagonal prism is a prism with six rectangular faces and top and base as hexagonal.

    A hexagonal prism has

    • 8 faces
    • 12 vertices and
    • 18 edges

    (image will be uploaded soon)

    Volume of Hexagonal Prism = 3 x a x b x h

    Where

    a – Apothem length of the hexagonal prism.

    b – Base length of the hexagonal prism.

    h – Height of the hexagonal prism.

    Solved Examples

    Example 1 : Find the volume of the triangular prism given below.

    (image will be uploaded soon)

    Solution:

    Given that a = Apothem length of a triangular prism = 9cm

    b = Base length of a triangular prism = 12 cm

    h = height of a triangular prism = 18cm

    We have, Volume of triangular prism = (

    1212

    ) a x b x h

    =

    1212

    x 9 x 12 x 18

    = 972

    cm3cm3

    So the volume of the triangular prism is 972 cubic centimeter.

    Example 2: Find the volume of rectangular prism given below.

    (image will be uploaded soon)

    Solution:

    Given that: l = length of a rectangular prism = 9cm

    b = Base of a rectangular prism = 7cm

    h = height of a rectangular prism = 13cm

    We have, Volume of Rectangular Prism = l x b x h

    = 9 x 7 x 13

    = 819

    cm3cm3

    Therefore the volume of rectangular prism is 819 cubic centimeters.

    Volume of a Prism.

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