Question

what is the volume of this figure? 4 cm 4 cm 8 cm 8 cm 12 cm 4 cm 14 cm cubic centimeters

Explanation:

Step1: Find volume of big rectangular prism

The big prism has length \( 14 \, \text{cm} \), width \( 4 \, \text{cm} \), height \( 12 \, \text{cm} \). Volume formula: \( V = l \times w \times h \).
\( V_{\text{big}} = 14 \times 4 \times 12 = 672 \, \text{cm}^3 \).

Step2: Find volume of the removed prism

The removed part has length \( 8 \, \text{cm} \), width \( 4 \, \text{cm} \), height \( 8 \, \text{cm} \).
\( V_{\text{removed}} = 8 \times 4 \times 8 = 256 \, \text{cm}^3 \).

Step3: Subtract to get final volume

\( V_{\text{final}} = V_{\text{big}} - V_{\text{removed}} = 672 - 256 = 416 \, \text{cm}^3 \).

Answer:

416