Answer:
23%
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*h
In 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 inches
The 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. So
V = 11.5*4.5*6.5 = 336.375
Error of 420 - 336.375 = 83.625
As 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. So
V = 12.5*5.5*7.5 = 515.625
515.625 - 420 = 95.625
As a percent, the error is of (95.625/420)*100 = 22.7% = 23%