So it basically sum of volume of 10 trapezoid prism. So, area of a floor y = area of the ceiling of the floor x, where y=x+1 So, basically we can find the vloume of 10 different trapezoid prism and sum them up. V= (1/2)*(Area of the floor  + area of its celing) * (height of the room) V=(15/2)*(Area of the floor+Area of the celing) [Notice that height of the room is the same for each floor=15 units) Total Volume= sum of all Vs. for instance, V1= (25+23)* (15) cubic units     =360 unit^3. So your total volume should be 2190 cubic units.

geshe · Apr 26, 2012 3:21 PM

Thanks much, is there anyway we can solve this problem via intragal method?

comingsoon · Apr 26, 2012 3:59 PM

The volume of each floor is calculated as  Where l represents the lenght of the floor, w is for the width and h is the height. You have the area of each floor, and also the height. The area of the floor is caculated as  So if you use this equation in the first I gave to you, one can obtain this: The volume for each floor is then calculated with the data you gave in the problem. For example, for the first floor you have Area=25 ft. and Height=15 ft. The volume of the first floor is then V=A*h=(25 ft.)*(15 ft.)=375 square feet Calculating for the rest of the floors: Floor number  Area (ft.) Height (ft.) Volume (sq ft.) Ground  25 15 375 2 23 15 345 3 20 15 300 4  18 15 270 5 16 15 240 6 14 15 210 7 12 15 180 8 10 15 150 9 9 15 135 10 8 15 120 Roof 7 15 105 Then you calculate the total volume of the building, summing the volume column of the table. The total volume of the building is 2430 square feet.  

Sparty · Apr 26, 2012 4:06 PM

 This could be Reimann sum which is part of calculus 1. Are you taking Calc 3?

geshe · Apr 26, 2012 4:25 PM

this there is no function given nor we have any addition information igven, we need to do reimann sum. I think taking volume of trapeziod prism will be better than taking cuboids.

geshe · Apr 26, 2012 4:33 PM

yas this is cal II problem? that will be great if you show me process of Reimann sum.

comingsoon · Apr 26, 2012 4:53 PM

 hint; here delta x= delta height = 15/2 anf f(x) =(1/2) of ( bottom area+ top area) Last edited: 26-Apr-12 05:09 PM

geshe · Apr 26, 2012 5:09 PM

@geshe BIG thanks for your help. I wanna share my happiness with you that I got 99 on that 'home exam' paper. Thanks.

comingsoon · May 3, 2012 9:55 PM

Wow 99 is a really good grade!!!! Congratulation!!! I am really happy for you Last edited: 03-May-12 11:18 PM

Geshe · May 3, 2012 11:17 PM