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Three Ways to Find the Volume of Pyramids

volume of pyramid: Image that shows the slant height of a pyramid

The volume of a pyramid is the number of cubic units inside the pyramid.

Before we go over calculating this volume, let’s review what a pyramid is. A pyramid is a three-dimensional figure where the base of the pyramid is connected to its point (or vertex) by triangular faces. Each of these triangles is called a lateral face, and the distance from the vertex of the pyramid to the base is considered to be the pyramid's height.

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How Does the Surface Area Definition Apply to 3D Objects?

Images showing the surface area definition of a pyramid, cube and rectangular prism

With three-dimensional shapes, the surface area of the object is defined as the total surface area, or the sum of the areas, on every outward surface. (This is different from the lateral surface area, which excludes the base and top of 3-D shapes).

Just like the area of a two-dimensional shape, the surface area definition is measured in square units. Depending on the shape and surface of the object, there are different surface area formulas to keep in mind. We’ll go through the surface area of each shape in turn.

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What Is the Slope of a Vertical Line?

what is the slope of a vertical line: Slope of a horizontal line graph

“What is the slope of a vertical line?” is a common question when you start to analyze graphs and linear equations. To answer that, let’s go back to the basic definition.

Slope is defined as the steepness, incline, or gradient of a line. It is also defined as the change in y value ("rise") over the change in x value ("run"). The slope formula is:

what is the slope of a vertical line: Slope formula

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How to Write and Apply the Standard Form of a Linear Equation

The standard form of a linear equation is a way of writing linear functions with x and y on the same sides of the equation.

A linear function is any math equation that includes an x- and y-value and can be represented on a graph. Writing a linear equation in standard form makes it easier to find the x and y-intercepts, which is where the graph crosses the x- and y-axis.

Here is an example of the standard form of a linear equation:

Example of the standard form of a linear equation

In the standard form of a linear equation, coefficients A, B, and C must all be integers (whole numbers without fractions or decimals), and A must always be a positive number.

The following equation of a line is written in standard form:

Standard form of a linear equation using whole numbers

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How To Create an Absolute Value Graph

Absolute value graphs are linear representations of absolute value functions. These equations are always expressed within absolute value bars. Here is an example:

Absolute value graph: Absolute value functions equation

Taking the absolute value of a number or equation cancels out its negative signs. Even though there is a -1 in the equation above, the x-intercept would be (1,0) since anything within absolute value bars becomes positive.

When graphing absolute value equations, the shape will either be an upright or upside-down V. The point where the "V" meets represents the vertex of the graph. Let's create a graph of the absolute value function above:

Absolute value function graph

From this graph, we can determine that the vertex of this equation is (1,0), the y-intercept is (0,2), and the graph opens upward.

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