Volume of a Pyramid Formula Explained 1 3 Base Area x Height Geometry Basics

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Volume of a Pyramid Formula Explained 1 3 Base Area x Height Geometry Basics

CodeLucky · ⏱ 3:36 · 318 مشاهدة · 5 months ago

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Hello and welcome. In this geometry lesson, we will explore the volume of pyramid. We will focus on the fundamental formula 1/3 multiplied by the base area multiplied by the height. First, let us define what pyramid is. pyramid is three-dimensional shape that has polygon as its base. This base can be triangle, square, or any other polygon. The sides of the pyramid are triangular faces that meet at single point at the top which is called the apex. The height is the straight vertical distance from the center of the base directly up to the apex. To understand the volume of pyramid, it is helpful to look at its corresponding prism. prism has two identical bases connected by vertical sides. rectangular prism, for example, has the same rectangular base at the bottom and the top. The volume of any prism is simply the area of its base multiplied by its height. the prism, it would fit perfectly within the height constraints, but it clearly occupies much less space. The question is exactly how much less space does it take up? There is consistent mathematical relationship here. It takes exactly three pyramids to fill the volume of one corresponding prism. If you filled hollow pyramid with water and poured it into the prism, you would need to do this three times to fill the prism completely. Since we know the volume of prism is the base area time the height and we know that prism holds the contents of three pyramids. We can derive the formula. The volume of one pyramid is simply 1/3 of the volume of the prism. Here is the official formula. Volume= 1/3 * * In this equation, capital stands for the area of the base and small stands for the vertical height of the pyramid. critical detail to remember is which height to use. You must always use the vertical height, which is the straight line from the apex to the center of the base. Do not use the slant height, which is the length of the diagonal side. Using the slant height will give you an incorrect answer. Let's work through an example with square pyramid. Suppose the side of the square base is 6 cm and the vertical height is 10 cm. First, calculate the base area. 6 * 6 = 36 cm. Next, apply the formula 1/3 of 36 * 10. 1/3 of 36 is 12. Finally, 12 * 10 gives us total volume of 120 cm. To summarize, remember that pyramid's volume is always 1/3 of the volume of prism with the same base and height. The formula is 1/3* base area time height. Always calculate the area of the base first and ensure you are using the vertical height. If you like this video, hit that like button and don't forget to subscribe. Visit codelucky.com for more such useful content.