I need some help I don't understand this question at all Geometry: Error and Precision in Measurement

Question

Sally has a Plexiglas cube that she believes is 100 cm wide, 100 cm long, and 100 cm tall, but in reality, the cube is actually 1% wider, 1% longer, and 1% taller than she believes. In other words, Sally’s cube is actually 101 cm wide, 101 cm deep, and 101 cm tall.

A. Since Sally believes the cube is 100 cm by 100 cm by 100 cm, she calculates that the vol-ume of her cube is 1,000,000 cm3. What per-cent greater is the actual volume of the cube than Sally’s calculation of the volume of the cube? Is the actual volume of Sally’s cube 1% greater than her calculated volume, or is it larger by some different percent?

B. Answer the following questions based on your answer to part (a): In general, if you want to know the volume of a cube to within 1% of its actual volume, will it be good enough to know the lengths of the sides of the cube to within 1% of their actual lengths? If not, will you need to know the lengths more accurately or less accurately?

Answer 1

a) Since she underestimated the length of all 3 sides, there is a cubic factor of error. In other words, if her volume calculation is V, the actual volume is:

V* = (1.01)³V = 1.0303V

Therefore, the actual volume is 3.03% greater than her calculated volume.

b) From the first part, we see that we need a greater level of accuracy to attain 1% error in volume.