Final answer:
The formula v = 1/5 (s²h) for the volume of a piece of a right square prism cut into 5 equal pieces can be rearranged to solve for side length s, yielding the solution s = √(5v/h).
Step-by-step explanation:
The student is asking to solve for the side length s of a right square prism given that the volume v of each piece, when the prism is cut into 5 equal pieces parallel to its bases, is v= 1/5 (s²h). To find s, we need to manipulate the formula. Rearranging the equation, we multiply both sides by 5 to get 5v = s²h. Since we are solving for s, we then divide both sides by h, which gives us 5v/h = s². Finally, we take the square root of both sides to isolate s, resulting in s = √(5v/h). In this way, the student can find the side length of the prism if the volume v and the height h of each piece are known.