The formula for the volume of a prism is V = base area x height, and for a pyramid it is V = (1/3) x base area x height.
First, calculate the base area of both shapes:
Base area of prism = (1/2) x 4cm x 6cm = 12cm2
Base area of pyramid = (1/2) x 4cm x 6cm = 12cm2
Now, calculate the volume of each shape:
Volume of prism = 12cm2 x 9cm = 108cm3
Volume of pyramid = (1/3) x 12cm2 x 9cm = 36cm3
Therefore, the correct answer is:
D: prism: 108cm3; pyramid: 36cm3