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) - \left\frac{1}{3}\
ight(8)(6)(6)\\)
○ \\((8)(6)(4) - \left\frac{1}{3}\
ight(8)(6)(10)\\)

Explanation:

Step1: Volume of a pyramid

The formula for the volume of a pyramid is $V_{pyramid}=\frac{1}{3}lwh$. The base of the pyramid has length $l = 8$, width $w = 6$, and height of the pyramid $h=10 - 4=6$. So $V_{pyramid}=\frac{1}{3}(8)(6)(6)$.

Step2: Volume of a rectangular prism

The formula for the volume of a rectangular prism is $V_{prism}=lwh$. Here, $l = 8$, $w = 6$, and $h = 4$. So $V_{prism}=(8)(6)(4)$.

Step3: Volume of the composite figure

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

Answer:

$\frac{1}{3}(8)(6)(6)+(8)(6)(4)$ (the first option)