Difference between revisions of "Calculate the Volume of a Pyramid"
(importing article from wikihow) |
m (Text replacement - "== Video ==" to "") |
||
| (6 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | + | <p>To calculate the volume of a pyramid, use the formula <math>V = \frac{1}{3}lwh</math>, where ''l'' and ''w'' are the length and width of the base, and ''h'' is the height. You can also use the equivalent formula <math>V = \frac{1}{3}A_{b}h</math>, where <math>A_{b}</math> is the area of the base and ''h'' is the height. The method varies slightly depending on whether the pyramid has a triangular or a rectangular base. If you want to know how to calculate the volume of a pyramid, just follow these steps.</p> | |
| − | [[Category:Volume]] | + | [[Category: Volume]] |
== Steps == | == Steps == | ||
| Line 11: | Line 11: | ||
#* <math>l = 4\,\text{cm}</math> | #* <math>l = 4\,\text{cm}</math> | ||
#* <math>w = 3\,\text{cm}</math> | #* <math>w = 3\,\text{cm}</math> | ||
| − | #Multiply the length and width to find the area of the base. To get the area of the base, simply multiply 3 cm by 4 cm.<sup>2</sup><ref>http://www.mathsteacher.com.au/year10/ch14_measurement/25_pyramid/21pyramid.htm</ref> | + | #Multiply the length and width to find the area of the base. To get the area of the base, simply multiply 3 cm by 4 cm.<sup>2</sup><ref name="rf1">http://www.mathsteacher.com.au/year10/ch14_measurement/25_pyramid/21pyramid.htm</ref> |
#*''Remember, <math>V = \frac{1}{3}A_{b}h</math>, so you need to know <math>A_{b}</math>. You can find this by plugging in <math>l = 4\,\text{cm}</math> and <math>w = 3\,\text{cm}</math> from the previous step.'' | #*''Remember, <math>V = \frac{1}{3}A_{b}h</math>, so you need to know <math>A_{b}</math>. You can find this by plugging in <math>l = 4\,\text{cm}</math> and <math>w = 3\,\text{cm}</math> from the previous step.'' | ||
#* <math>A_{b} = lw</math> | #* <math>A_{b} = lw</math> | ||
| Line 25: | Line 25: | ||
#* <math>V = (\frac{1}{3})(48\,\text{cm}^3)= 16\,\text{cm}^3</math> | #* <math>V = (\frac{1}{3})(48\,\text{cm}^3)= 16\,\text{cm}^3</math> | ||
===Pyramid with a Triangular Base=== | ===Pyramid with a Triangular Base=== | ||
| − | #Find the length and width of the base. The length and width of the base ''must'' be perpendicular to each other for this method to work. They can also be considered the base and height of the triangle. In this example, the width of the base is 2 cm and the length of the triangle is 4 cm.<ref | + | #Find the length and width of the base. The length and width of the base ''must'' be perpendicular to each other for this method to work. They can also be considered the base and height of the triangle. In this example, the width of the base is 2 cm and the length of the triangle is 4 cm.<ref name="rf1" /> |
#*If the length and width are not perpendicular and you don't know the height of the triangle, there are a few other methods you can try to [[Calculate the Area of a Triangle|calculate the area of a triangle.]] | #*If the length and width are not perpendicular and you don't know the height of the triangle, there are a few other methods you can try to [[Calculate the Area of a Triangle|calculate the area of a triangle.]] | ||
#*''Remember, <math>V = \frac{1}{3}lwh = \frac{1}{3}A_{b}h</math>, so you need to know <math>l</math> and <math>w</math> first.'' | #*''Remember, <math>V = \frac{1}{3}lwh = \frac{1}{3}A_{b}h</math>, so you need to know <math>l</math> and <math>w</math> first.'' | ||
| Line 46: | Line 46: | ||
#*<math>V = (\frac{1}{3})(20\,\text{cm}^3)= 6.67\,\text{cm}^3</math> | #*<math>V = (\frac{1}{3})(20\,\text{cm}^3)= 6.67\,\text{cm}^3</math> | ||
| − | + | ||
| − | + | ||
== Tips == | == Tips == | ||
