How to Calculate the Volume of a Pyramid

Step-by-Step Guide

1. 1

   Step 1: Find the length and width of the base.

   In this example, the length of the base is 4 cm and the width is 3 cm.
   
   If you're working with a square base, the method is the same, except the length and width of the square base will be equal.
   
   Write down these measurements.
   
   Remember, V=13lwh=13Abh{\displaystyle V={\frac {1}{3}}lwh={\frac {1}{3}}A_{b}h}, so you need to know l{\displaystyle l} and w{\displaystyle w} first. l=4cm{\displaystyle l=4\,{\text{cm}}} w=3cm{\displaystyle w=3\,{\text{cm}}} , To get the area of the base, simply multiply 3 cm by 4 cm.2Remember, V=13Abh{\displaystyle V={\frac {1}{3}}A_{b}h}, so you need to know Ab{\displaystyle A_{b}}.
   
   You can find this by plugging in l=4cm{\displaystyle l=4\,{\text{cm}}} and w=3cm{\displaystyle w=3\,{\text{cm}}} from the previous step.
   
   Ab=lw{\displaystyle A_{b}=lw} Ab=(4cm)(3cm)=12cm2{\displaystyle A_{b}=(4\,{\text{cm}})(3\,{\text{cm}})=12\,{\text{cm}}^{2}} , The area of the base is 12 cm2 and the height is 4 cm, so you can multiply 12 cm2 by 4 cm.
   
   Remember, V=13Abh{\displaystyle V={\frac {1}{3}}A_{b}h}, so you need to know Abh{\displaystyle A_{b}h}.
   
   You can find this using Ab{\displaystyle A_{b}} from the previous step.
   
   Ab=12cm2{\displaystyle A_{b}=12\,{\text{cm}}^{2}} h=4cm{\displaystyle h=4\,{\text{cm}}} Abh=(12cm2)(4cm)=48cm3{\displaystyle A_{b}h=(12\,{\text{cm}}^{2})(4\,{\text{cm}})=48\,{\text{cm}}^{3}} , Or, in other words, divide by
   3.
   
   Remember to state your answer in cubic units whenever you're working with three-dimensional space.
   
   Remember, V=13lwh=13Abh{\displaystyle V={\frac {1}{3}}lwh={\frac {1}{3}}A_{b}h}.
   
   You can plug in Abh=48cm3{\displaystyle A_{b}h=48\,{\text{cm}}^{3}} from the previous step.
   
   V=13Abh{\displaystyle V={\frac {1}{3}}A_{b}h} V=(13)(48cm3)=16cm3{\displaystyle V=({\frac {1}{3}})(48\,{\text{cm}}^{3})=16\,{\text{cm}}^{3}}
2. 2

   Step 2: Multiply the length and width to find the area of the base.

3. 3

   Step 3: Multiply the area of the base by the height.

4. 4

   Step 4: Multiply your result so far by 13{\displaystyle {\frac {1}{3}}}.

Detailed Guide

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