Question

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.

Answer 1

the picture is sideways sorry

Answer 2

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

Answer 3

Thank you soooooo much (:

Answer 4

You're welcome! :) Good luck with math!

Answer 5

wait but isnt 96 the height of the building?

Answer 6

I guessed 96 and 40 were the sides of the building. As in the sides of the square. Isn't that what the question means?

Answer 7

The courtyard measure 40 feet on a side. I just dont understand this question

Answer 8

Me too. Lol.