The volume of a right rectangular prism is given by the formula V = lwh, where l, w, and h represent the length, width, and height of the prism, respectively. Since the prism is right and rectangular, the length and width are perpendicular to each other.
We are given that the height of the prism is 17.5 centimeters and the area of the base is 18 square centimeters. Since the base is rectangular, we can find the length and width by dividing the area by one of the dimensions and multiplying by the other. Let's say the length is x and the width is y, then:
xy = 18 (area of base)
y = 18/x (solve for y)
Now, we can substitute the value of y in terms of x into the formula for the volume:
V = lwh = xyh = (18/x)(x)(17.5) = 315 cubic centimeters
Therefore, the volume of the right rectangular prism is 315 cubic centimeters.