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Volume in Geometry Examples




 
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More Lessons for High School Geometry

Math Worksheets

A series of free, online High School Geometry video, lessons and solutions.
Videos, worksheets, and activities to help Geometry students.

In this lesson, we will learn

  • how to calculate the volume of a pyramid
  • how to solve equations with squares and cubes
  • how to calculate the volume of a sphere
  • how to calculate the surface area of a sphere


Volume of Pyramid

The formula for the volume of prisms can also be applied to the volume of pyramids, which occupy only one third of the space of a corresponding prism with the same base and height. To calculate the volume of a pyramid, we simply multiply the area of the one of the bases times one third of the height of the pyramid. This formula is very similar to volume of cylinder and volume of cone formulas.

How to find the volume of a square pyramid and a triangular pyramid. Also compare how they are the same and how they are different.
Find the volume of the pyramid
The formula for the volume of a pyramid is 1/3 x base x height.
Watch this video to discover how to use this formula to find the volume of a pyramid.



Solving Equations with Squares and Cubes

Many of the formulas for calculating volumes (prism volume, volume of cylinders, volume of cones formulas and volume of pyramids) require solving equations with square roots or cube roots. To solve these equations, we use many of the same principles that we learned when solving equations with square roots in Algebra such as isolating the unknown variable and simplifying

How to solve equations using square roots or cube roots.

Volume of Sphere

To find the volume of a sphere, we can calculate the volume by using a simple volume formula where we multiply 4/3 by pi by the radius cubed. The volume of sphere formula is unique because it only requires the radius to calculate the volume of any sphere. When finding the volume of spheres, it is important to note if we are given the radius or the diameter of the shape. This formula is very similar to other prism volume formulas.

Volume of a Sphere


 
How to calculate the volume of a sphere.

Surface Area of a Sphere

In general, surface area is the sum of all the shapes that cover the surface of an object. To calculate the surface area of a sphere we multiply 4 by pi by the radius of the sphere squared. Given this formula, we can find the surface area of a sphere when given the radius. Similarly, we can find the radius of a sphere is we are given the surface area. This formula is very similar to other prism volume formulas.

How to Find the Surface Area of a Sphere.
How to find the surface area of a sphere using the formula SA = 4(pi)(r)2


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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