Answer:
225 cubic centimeters
Explanation:
The formula for the volume of a rectangular pyramid is V = (1/3)Bh, where B is the area of the base and h is the height. The base of the rectangular pyramid is a rectangle with the same length and width as the rectangular prism. Let's call the length, width, and height of both shapes "l", "w", and "h", respectively. Then:
V_pyramid = (1/3)B_pyramid * h
75 = (1/3)(lw) * h
We also know that the rectangular prism has the same length, width, and height as the rectangular pyramid, so its volume can be calculated using the formula V_prism = lwh:
V_prism = lwh
V_prism = lwh = l * w * h
Since l = w = h in this case, we can simplify this to:
V_prism = l * w * h = l^3
We can use the equation for the volume of the rectangular pyramid to solve for h:
75 = (1/3)(lw) * h
225 = lw * h
h = 225/(lw)
Substituting this value for h into the equation for the volume of the rectangular prism gives:
V_prism = l^3 = l * w * (225/(lw))
V_prism = 225 cubic centimeters
Therefore, the volume of the rectangular prism is 225 cubic centimeters.