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Which Angles Relate to Parallel Lines and Transversals?

parallel lines and transversals: vertical angles

Image credit: Desmos

Parallel lines and transversals are two important geometry concepts because they result in special angle relationships you’ll find in different postulates and theorems and use for solving geometry proofs.

First, two definitions:

Parallel lines: Never intersect, or cross, one another

Transversal line: Intersects two or more lines or line segments

When a transversal line crosses a pair of parallel lines, many types of angles can be created. Let’s go over the many different pairs of angles created by parallel lines and transversals:

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Calculating the Area and Volume of a Right Circular Cone

volume of a right circular cone: cone

Let’s get right to it — we’re here to calculate the surface area or volume of a right circular cone. As you might already know, in a right circular cone, the height goes from the cone’s vertex through the center of the circular base to form a right angle. Right circular cones are what we typically think of when we think of cones.

There are two right circular cone formulas to know: The formula for the volume of a cone is (𝛑r²h)/3. The formula for the surface area of a right circular cone is 𝛑rs+𝛑r². Let's look at them both in further detail.

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Your Step-by-Step Guide to Finding the Volume of a Cone

volume of a cone: cones with different colors

Finding the volume of a cone means determining the full amount of space that this three-dimensional figure takes up. Just like when you find the volume of a cylinder or sphere, there is a cone formula that you must use to find its volume. You’ll need to know the radius of the base of a cone and the height of a cone to find the volume.

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How to Find the Volume of a Half Sphere

how to find volume of half sphere: 3D sphere in half

Understanding how to find the volume of a half sphere, or in other words, the volume of a hemisphere, is easier than it seems. Keep in mind that volume is the amount of space that a three-dimensional shape takes up, whereas the surface area is the total area of all the surfaces of that three-dimensional shape.

First, we need to review the formula for the volume of the sphere. The volume formula for a sphere is (4𝛑r²)/3, where r stands for the radius of the sphere. (The radius is the distance from the center of the sphere).

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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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