Question

which expression represents the volume, in cubic units, of the composite figure?
○ $\frac{1}{3}(8)(6)(6)+(8)(6)(4)$
○ $\frac{1}{3}(8)(6)(10)+(8)(6)(4)$
○ $(8)(6)(4)-\frac{1}{3}(8)(6)(6)$
○ $(8)(6)(4)-\frac{1}{3}(8)(6)(10)$

Explanation:

Step1: Identify component - shapes

The composite figure is made of a rectangular - prism and a rectangular - pyramid.

Step2: Recall volume formulas

Volume of a rectangular prism \(V_{prism}=l\times w\times h\), and volume of a rectangular pyramid \(V_{pyramid}=\frac{1}{3}\times l\times w\times h\). Here, for the prism, \(l = 8\), \(w = 6\), \(h = 4\), so \(V_{prism}=(8)(6)(4)\). For the pyramid, the base has length \(l = 8\) and width \(w = 6\), and height \(h=10 - 4=6\), so \(V_{pyramid}=\frac{1}{3}(8)(6)(6)\).

Step3: Find volume of composite figure

The volume of the composite figure \(V = V_{pyramid}+V_{prism}=\frac{1}{3}(8)(6)(6)+(8)(6)(4)\).

Answer:

\(\frac{1}{3}(8)(6)(6)+(8)(6)(4)\)