If % error in the sides of cube is 3 % then % error in the vol of the cube is
Answers
Explanation:
1
If the percentage error in the side is a cube is 3%, what is the percentage error in its volume?
Martyn Hathaway
Answered March 21, 2018
If the percentage error in the side is a cube is 3% what is the percentage error in its volume?
Your question is open to interpretation!
When you say that the error is in the side, do you mean that the error occurs in:
the length of one edge; or
the area of one face
In either case, the resultant object would no longer be a cube. So, perhaps, you mean that the error occurs in the length of all 12 edges or the area of all 6 faces. Further, these errors must all be in the same “direction” - e.g. if you increase the area of some faces by 3% and decrease others by 3%, you would no longer have a cube.
First case - we will assume that the error is in the length of the edges.
If the cube is supposed to have edges of length x , its volume would be x3.
If we increase the length of the edges by 3%, the actual length of each edge would be 1.03x , thus the volume would be (1.03x)3=1.092727x3
Subtracting the volume it is supposed to have, we have an error of 0.092727x3 . Dividing this by the volume it is supposed to have, the error is 0.092727 i.e. 9.2727 .
If the error was a decrease, then each edge would have a length of 0.97x thus the volume would be (0.97x)3=0.912673x3
The decrease in volume = (1−0.912673)x3=0.087327x3 . Dividing this by the volume it is supposed to have, we have an error of 0.087327 , i.e. 8.7327 .
Second case - we will assume that the error is in the area of each face.
If the area of each face increases by 3% then, as each face must remain square, this means than each edge must increase by 1.03−−−−√x≈0.014889x . Thus the volume would be approximately (1.014889x)3≈1.045336x3 . This equates to an approximate increase in volume of 4.5336 .
If the area of each face decreases by 3%, then each edge must have a length of 0.97−−−−√x≈0.984886x . Thus the volume would be approximately (0.984886x)3≈0.955339x3 . This equates to an approximate decease of 4.4661 .
Explanation:
The correct ans is 4.4661