Solid geometry is concerned with three-dimensional shapes. In these lessons, we will learn
A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. A prism is named after the shape of its base.
The other faces are in the shape of parallelograms. They are called lateral faces.
The following diagrams show a triangular prism and a rectangular prism.
A right prism is a prism that has its bases perpendicular to its lateral surfaces. If the bases are not perpendicular to its lateral bases then it is called an oblique prism.
When we cut a prism parallel to the base, we get a cross section of a prism. The cross section has the same size and shape as the base.
What is a prism and distinguishes between a right prism and an oblique prism?
How to label the parts of a prism and how to distinguish between an oblique and a right prism?
The volume of a right prism is given by the formula:
Volume = Area of base × height = Ah
where A is the area of the base and h is the height or length of the prism.
Worksheet to calculate volume of prisms and pyramids.
Find the volume of the following right prism.
Volume = Ah
= 25 cm2 × 9 cm
= 225 cm3
Find the volume of the following right prism
First, we need to calculate the area of the triangular base.
We would need to use Pythagorean theorem to calculate the height of the triangle.
h2 + 32 = 52
Area of triangle =
= × 6 × 4
= 12 cm2
Volume of prism = Ah
= 12 cm2× 8 cm
= 96 cm3
How to find the volume of a rectangular and a triangular prism?
Step 1: Find the area of the base.
Step 2: Multiply the area of the base times the height.
How to find the volume of any prism, right or oblique using a general formula?
The following video shows how to solve a word problem involving the volume of prisms.
Find the volume and capacity of a swimming pool which is made up of a rectangular and trapezoidal prism.
Use the given net to determine the surface area and volume of a triangular prism
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