SOLUTION: an architect created a plan for a four-story building with a central courtyard. The building measures 96 ft on each side. The courtyard measures 40 ft on a side. His clients asked

Question 1141393: an architect created a plan for a four-story building with a central courtyard. The building measures 96 ft on each side. The courtyard measures 40 ft on a side. His clients asked him to work on an alternative design with the same volume but without the courtyard, Find the side length of such a building if it is designed as a four-story square prism.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
an architect created a plan for a four-story building with a central courtyard.
The building measures 96 ft on each side.
The courtyard measures 40 ft on a side.
His clients asked him to work on an alternative design with the same volume but without the courtyard,
Find the side length of such a building if it is designed as a four-story square prism.
:
find the volume of the original plan (assume the height of the 4 story building is 40')
(96*96*40) - (40*40*40) = 304,640 cu/ft is volume of the building
:
let s = the side of the new building
s^2 * 40 = 304640
s^2 = 304640/40
s^2 = 7616
s =
s = 87.27 ft on each side
:
:
Check
87.27 * 87.27 * 40 = 304,642.116 ~ 304,640

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