An architect created a plan for a four story building with a central courtyard.
The building measures 96 feet on each side. The courtyard measure 40 feet on a side. His clients asked him to work out 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.
Any help would be wonderful thanks.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Hi! :) Well, let's get the volume of the hollow prism first. Let h be the height of the building. The rectangular prism without the courtyard would has a volume of (96 ft)(96 ft)(h ft)=9216h ft^3. Now, with the courtyard, imagine cutting out the center of a sytrofoam box. The volume would then be the original minus the removed center. Therefore, the volume of the building WITH the courtyard would have to be VOL w/o courtyard - VOL of courtyard = VOL of initial plan of architect. The volume of the courtyard is (40 ft)(40 ft))(h ft)=1600h ft^3. VOL of initial plan, therefore, is 7616h ft^3.
From there, we can answer the problem. The side length is asked. Without any courtyard, we want to achieve the same volume as before.
Let s be the side length.
7616h ft^3 = (s ft)(s ft)(h ft)
7616h ft^3 = (s^2)(h) ft^3
7616 = s^2
s= sqrt (7616) ft