The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic centimeters. 108 cubic centimeters 96 cubic centimeters 120 cubic centimeters 48 cubic centimeters

To find the volume of the solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it, we need to follow these steps:Step 1: Calculate the volume of the original solid rectangular prism without the hole.The volume (V) of a rectangular prism is calculated by multiplying its length (L), width (W), and height (H):\[V = L \times W \times H\]Given the dimensions of the original solid rectangular prism:Length (L) = 12 cmWidth (W) = 3 cmHeight (H) = 3 cm\[V_{\text{original}} = 12 \text{ cm} \times 3 \text{ cm} \times 3 \text{ cm}\]\[V_{\text{original}} = 36 \text{ cm} \times 3 \text{ cm}\]\[V_{\text{original}} = 108 \text{ cm}^3\]Step 2: Calculate the volume of the hole, which is also a rectangular prism.The hole is described as having a square with a side length of 1 cm on the front face and on the top face. This means the hole is a square prism (or a cube in this case) with the following dimensions:Side length = 1 cmThe volume (V_hole) of a cube is calculated by cubing the side length (s):\[V_{\text{hole}} = s^3\]Given the side length of the hole:Side length (s) = 1 cm\[V_{\text{hole}} = 1 \text{ cm} \times 1 \text{ cm} \times 1 \text{ cm}\]\[V_{\text{hole}} = 1 \text{ cm}^3\]Step 3: Subtract the volume of the hole from the volume of the original solid to find the volume of the solid with the hole.\[V_{\text{solid with hole}} = V_{\text{original}} - V_{\text{hole}}\]\[V_{\text{solid with hole}} = 108 \text{ cm}^3 - 1 \text{ cm}^3\]\[V_{\text{solid with hole}} = 107 \text{ cm}^3\]However, the options provided do not include 107 cubic centimeters. This suggests there might be an error in the interpretation of the question or the picture details. If the hole goes through the center of the solid, it would extend the entire length or height of the prism, not just 1 cm. Therefore, we need to consider the hole as a rectangular prism that extends through the entire length or height of the original prism.If the hole extends through the entire length of the prism (12 cm), then the volume of the hole would be:\[V_{\text{hole}} = \text{side length}^2 \times \text{length of the prism}\]\[V_{\text{hole}} = 1 \text{ cm}^2 \times 12 \text{ cm}\]\[V_{\text{hole}} = 12 \text{ cm}^3\]Then the volume of the solid with the hole would be:\[V_{\text{solid with hole}} = V_{\text{original}} - V_{\text{hole}}\]\[V_{\text{solid with hole}} = 108 \text{ cm}^3 - 12 \text{ cm}^3\]\[V_{\text{solid with hole}} = 96 \text{ cm}^3\]Therefore, the correct answer is:96 cubic centimeters.