Final answer:
The new volume of the right square pyramid, where the sides of the base are multiplied by 3 while the height remains fixed, is 108 cubic centimeters.
Step-by-step explanation:
The volume of a right square pyramid is calculated using the formula V = (1/3) Ab h, where Ab is the area of the base and h is the height of the pyramid. Since the base of our pyramid is a square, the area of the base (Ab) can be expressed as s2, where s is the side of the square. This gives us the volume formula V = (1/3) s2 h.
Given the original volume is 12 cubic centimeters, when the sides of the base are multiplied by 3, our new side length becomes 3s. Using the volume formula, the new volume V' will therefore be: V' = (1/3) (3s)2 h. Simplifying this gives us V' = (1/3) 9s2 h, meaning the new volume is 9 times the original volume since the height remains unchanged. Thus, the new volume will be 108 cubic centimeters.