Explanation:
The volume of a rectangular prism is given by:
V_prism = length x width x height
Substituting the given values, we get:
V_prism = 12 cm x 6 cm x 8 cm
V_prism = 576 cm^3
The volume of a rectangular pyramid is given by:
V_pyramid = (1/3) x base area x height
The base of the pyramid is a rectangle with length and width equal to the base of the prism, which is 12 cm and 6 cm. Therefore, the base area is:
base area = length x width = 12 cm x 6 cm = 72 cm^2
Substituting the given and calculated values, we get:
V_pyramid = (1/3) x 72 cm^2 x 18 cm
V_pyramid = 432 cm^3
The total volume of the composite space figure is the sum of the volumes of the prism and the pyramid:
V_total = V_prism + V_pyramid
V_total = 576 cm^3 + 432 cm^3
V_total = 1008 cm^3
Therefore, the volume of the composite space figure is 1008 cm^3. The answer is C. 1008 cm^3.