Chapter 11.3, Problem 5P

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 om deep, and 101 cm tall. ‘

1. Since Sally believes the cube is 100 cm by 100 cm by 100 cm. she calculates that the volume of her cube is 1,000,000 $C{M}^3$ . What percent 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?

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, wnll it be good enough to know the lengths of the sudes of the cube to Within 1% of their actual lengths? If not, will you need to know the lengths more accurately or less accurately?