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How to Find the Volume of a Sphere With One Formula

Before determining how to find the volume of a sphere, you must first understand the structure of a sphere. A sphere is a three-dimensional circle:

how to find volume of sphere: center point of a sphere

The center of a sphere is marked by a point, similar to the nucleus of an atom. The radius r of the sphere represents how far away that given point is from the surface of the sphere. No matter which direction the radius of the sphere points, its length will always reach the outside surface of the sphere.

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How to Find Volume and Surface Area for 6 Common Shapes

volume and surface area: Chart of different shapes and areas with formulas

Our world is filled with three-dimensional objects. When it comes to knowing the volume and surface area of these objects, there are two definitions that you have to know. Surface area is the area of all outer facing surfaces on an object. The total surface area is calculated by adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object. This is done using different area formulas and measured in square units.

Volume is the amount of space that a three dimensional object takes up. There are also different formulas for different three-dimensional shapes. The total volume of an object is measured in cubic units.

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Vertical Angle Theorem: What It Is and How to Use It

The Vertical Angle Theorem says the opposing angles of two intersecting lines must be congruent, or identical in value. That means no matter how or where two straight lines intersect each other, the angles opposite to each other will always be congruent, or equal in value:

Vertical Angle Theorem: Graph showing two straight lines intersect each other

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How to Recognize Adjacent Supplementary Angles

adjacent supplementary angles: Figures showing different pairs of angles

In geometry, we give different names to different types of angles depending on the measure of the given angle: right angles, adjacent supplementary angles, vertical angles. But how do we know which is which?

Let’s start with the basics.

If the measure of the angle is exactly 90 degrees, it’s known as a right angle. If an angle is less than 90 degrees, it’s an acute angle. An angle greater than 90 degrees is an obtuse angle. If the measure of an angle is equal to 180 degrees, it’s known as a straight angle.

There are also names given to pairs of angles.

Vertical angles, or opposite angles, are the two angles directly opposite each other when two straight lines cross (Figure 1).

Complementary angles are two angles that add to 90 degrees (Figure 2).

Supplementary angles are two angles that add up to 180 degrees (Figure 3).

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What Is the Slope of a Horizontal Line?

what is the slope of a horizontal line: Graph with a green horizontal line

You might know what slope is, but when you’re asked “What is the slope of a horizontal line?”, your mind goes blank. We’ll walk you through this answer, where it comes from, and how to calculate slope in other situations.

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