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: Identify composite shapes

The figure is a rectangular prism + a rectangular pyramid.

Step2: Calculate prism volume

Volume formula: $V_{prism}=l\times w\times h$
$V_{prism}=8\times6\times4$

Step3: Calculate pyramid height

Pyramid height = total height - prism height
$h_{pyramid}=10-4=6$

Step4: Calculate pyramid volume

Volume formula: $V_{pyramid}=\frac{1}{3}l\times w\times h$
$V_{pyramid}=\frac{1}{3}(8)(6)(6)$

Step5: Sum volumes for total

Total volume = $V_{prism}+V_{pyramid}$

Answer:

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