Find the greatest possible percent error in calculating the volume of the prism.

Answer:23%Step-by-step explanation:Volume of a rectangular prism:A rectangular prism has three dimensions, which are the base b, the height h and the width w.The volume is:V = b*w*hIn this question:The base is 12 inches, so b = 12.The width is 5 inches, so w = 5.The height is 7 inches, so h = 7.The volume is:V = 12*5*7 = 420 cubic inches.With error:They are rounded to the nearest inch, so:The base can go from 12 - 0.5 = 11.5 to 12 + 0.5 = 12.5 inches.The width can go from 5 - 0.5 = 4.5 to 5 + 0.5 = 5.5 inchesThe height can go from 7 - 0.5 = 6.5 to 7 + 0.5 = 7.5 inches.Volume with the smallest values:We have that b = 11.5, w = 4.5, h = 6.5. SoV = 11.5*4.5*6.5 = 336.375Error of 420 - 336.375 = 83.625As a percent, the error is of (83.625/420)*100 = 19.9% Volume with the higher values:We have that b = 12.5, w = 5.5, h = 7.5. SoV = 12.5*5.5*7.5 = 515.625515.625 - 420 = 95.625As a percent, the error is of (95.625/420)*100 = 22.7% = 23%