## rachiesweet 3 years ago 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.

1. rachiesweet

the picture is sideways sorry

2. imagreencat

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

3. rachiesweet

Thank you soooooo much (:

4. imagreencat

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

5. rachiesweet

wait but isnt 96 the height of the building?

6. imagreencat

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?

7. rachiesweet

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

8. imagreencat

Me too. Lol.