Volume of Composite Prisms
Volume of Composite Prisms (second entry) is a Grade 5 math skill from Illustrative Mathematics Chapter 1 (Finding Volume) where students decompose composite 3D figures into individual rectangular prisms, calculate each prism's volume using V = l × w × h, and add the volumes to find the total. The formula V_total = V_prism1 + V_prism2 applies to L-shaped figures, T-shaped figures, and stepped platforms.
Key Concepts
To find the volume of a composite solid made of rectangular prisms, calculate the volume of each individual prism and then add their volumes together. $$V {\text{total}} = V {\text{prism 1}} + V {\text{prism 2}}$$.
Common Questions
How do you find the volume of a composite figure made of rectangular prisms?
Decompose the figure into non-overlapping rectangular prisms. Calculate the volume of each using V = l × w × h. Add all the volumes together for the total volume of the composite figure.
What is an example of finding composite prism volume?
An L-shaped figure split into a vertical prism (2×3×7 = 42 in³) and a horizontal prism (5×3×2 = 30 in³): total volume = 42 + 30 = 72 in³. A stacked figure: bottom (10×8×3 = 240 cm³) + top (5×8×4 = 160 cm³) = 400 cm³.
What chapter covers composite prism volume in Illustrative Mathematics Grade 5?
Volume of composite prisms is covered in Chapter 1 of Illustrative Mathematics Grade 5, titled Finding Volume.
How do you decide where to decompose a composite figure?
Look for natural break points where the figure changes shape. You can split horizontally or vertically as long as the resulting parts are non-overlapping rectangular prisms whose volumes sum to the whole figure's volume.
Can the same composite figure be decomposed in different ways?
Yes. Different decompositions give different individual prism volumes but always the same total. As long as the pieces are non-overlapping and cover the whole figure, any valid decomposition works.