A prism is a three-dimensional solid object with identical ends. Flat faces, identical bases, and equal cross-sections make up this combination. The prism’s faces are either parallelograms or rectangles without bases. And any n-sided polygon or a triangle could serve as the prism’s base.
What is the “Volume of Mixed Prisms Worksheet”?
This worksheet will explore some of the methods of finding the volume of composite prisms.
What is the volume of mixed prisms?
The bases of the prisms shown here have a variety of shapes, so knowing the formulas for their respective fields is a requirement before moving on. Divide the base’s area by its height.
How will the “Volume of Mixed Prisms Worksheet” help you?
This worksheet will help you the students to understand the particular topic. In any case, the fundamental approach to writing the prism volume formula is unchanged. You will discover how to determine any type of prism’s volume, just like with all three-dimensional shapes.
Instructions on how to use the “Volume of Mixed Prisms Worksheet”
Study the concept and examples given and try to solve the given exercises below. Keep reading to discover how to apply its formula using examples with solutions.
Any prism’s volume is a function of the base’s shape. The area of the base also changes as a result of the base’s changing shape.
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Volume of Mixed Prisms Worksheet (with answer key + PDF)
Volume of Prisms
The total amount of space occupied by a prism in three dimensions is known as its volume. Its mathematical definition is the sum of the base’s area and its length.
The general formula to find the volume of any prism is:
Volume (V) = Base Area × Height, here, the height of any prism is the distance between the two bases.
- The volume of a Triangular Prism
A triangular prism is a type of prism that has two triangular bases in addition to three rectangular faces. Given that a triangular prism’s cross-section is a triangle, the following formula can be used to calculate its volume:
The volume of a Triangular Prism = (½) abh cubic units.
a = Apothem length of a triangular prism
b = Base length of a triangular prism
h = height of a triangular prism
- The volume of a rectangular prism
A rectangular prism has two parallel rectangular bases and four parallel rectangular faces. We are aware that a rectangular prism has a rectangular cross-section. A “Cuboid” is another name for the rectangular prism.
The volume of a Rectangular Prism = l.b.h cubic units.
l = Base width of a rectangular prism
b = Base length of a rectangular prism
h = height of a rectangular prism
- The volume of a Pentagonal Prism
Five rectangular faces and two parallel pentagonal bases make up a pentagonal prism. Given that the pentagonal prism’s base area is (5/2) ab, the volume of the pentagonal prism is as follows:
The Volume of a Pentagonal Prism = (5/2) a.b.h cubic units
a = Apothem length of the pentagonal prism.
b = Base length of the pentagonal prism.
h = Height of the pentagonal prism
- The volume of a Hexagonal Prism
A hexagonal prism is a prism that has two parallel hexagonal bases and six rectangular faces. The formula to determine a hexagonal prism’s volume is as follows: where 3AB is the hexagonal prism’s base area.
The volume of a Hexagonal Prism = 3abh cubic units
a = Apothem length of the hexagonal prism.
b = Base length of the hexagonal prism.
h = Height of the hexagonal prism.
Volume of Mixed Prisms
Find the volume of each prism.
- Find the volume of a triangular prism whose base is 40 cm, height is 15 cm, and length is 60 cm.
- Find the volume of a rectangular prism whose width is 7 cm, height is 12 cm, and length is 16 cm.
- Find the volume of a pentagonal prism whose base is 6 cm, apothem is 4.13 cm, and height is 8 cm.
- Find the volume of a square prism whose base edge is 7 in, and whose length is 11 in.
- Find the volume of a trapezoidal prism whose base edges are 34 cm and 22 cm, vertical height is 12 cm, and length is 52 cm.
- Find the volume of a hexagonal prism whose base is 12 cm; apothem is 10.39 cm and height is 20 cm.
You can download this worksheet here.