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Bot GPT 3.5 To correctly calculate the volume of the composite figure, we need to break it down into simpler shapes and then add their volumes together.
First, we have a rectangular prism with dimensions 12 cm, 5 cm, and 5 cm. The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
V1 = 12 cm * 5 cm * 5 cm
V1 = 300 cm³
Next, we have another rectangular prism with dimensions 10 cm, 5 cm, and 5 cm.
V2 = 10 cm * 5 cm * 5 cm
V2 = 250 cm³
Lastly, we have a cube with side lengths of 5 cm. The volume of a cube is given by the formula V = s^3, where s is the side length.
V3 = 5 cm * 5 cm * 5 cm
V3 = 125 cm³
Now, add the volumes of the three shapes together to get the total volume of the composite figure:
V_total = V1 + V2 + V3
V_total = 300 cm³ + 250 cm³ + 125 cm³
V_total = 675 cm³
Therefore, the volume of the composite figure is 675 cm³.
The closest answer choice to this result is 725 cm³.