A rectangular prism has dimensions / w, and h. If the width is changed to 2w, how does the volume change?
a The volume is doubled. b. The volume is the same.
c. The volume is half as large
d. The volume is squared
b. The volume is the same.
The volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height. If only the width is changed to 2w, the volume formula remains the same, but the new dimensions of the prism are 2w, w, and h.
Thus, the new volume is V' = (2w)(w)(h) = 2w^2h.
Since 2w^2h is equivalent to 2(w^2h), it can be seen that the volume has not changed.