World's Fair Math Explanation Example

Surface Area and Volume of a Building

The Harold Washington Library is in the shape of a rectangular prism for the main building.  I want to find the surface area and volume of the building.  The surface area of is the total area of all the faces.  Surface area is measured in square units (cm²) because like area it is the amount of material that covers a flat surface and can be put into square units of measure.  The other measurement that I want to show is the volume which is the space inside the figure.  Volume is measured in cubic units (cm³) because it is measuring the units inside of a 3 dimensional figure. 

The HWL is approximately 50 feet long, 25 feet wide and 30 feet tall.

Surface area = Sum of all 6 of the rectangular faces 

SA= 2 (lxw) + 2 (lxh) +2 (wxh)

SA= 2 (50x25) + 2 (50x30) + 2(25x30)

SA = 2 (1,250) + 2 (1500) + 2 (750)

SA = 2,500 + 3000 + 1500

SA = 5,500 + 1500

Surface Area = 7,000 square feet  

I found the surface area of the rectangular prism by measuring the area of the 6 faces of the prism.  I knew there were 6 faces from the net drawing of a rectangular prism.  First I knew the building was 50 ft. length, 25 ft. width, and 30 ft. height and put them into the equation.  SA= 2 (lxw) + 2(lxh) + 2(wxh). I multiplied inside parentheses first.  For example, 50x25=1,250. Then I knew that the 2 on the outside meant to multiply since there was a number next to a parentheses.   So I multiplied 2 times 1,250 to get 2,500 using mental math. I multiplied by two because I knew the top and the bottom of the prism were the same size. The front and back sides were each 750 square feet, or 25 times 30, and the top and bottom were each 1,250 which was found by multiplying 50 by 25.  Then I doubled the front to find the total area of the front and back sides since they were both 25 by 30. 1500 times 2 equaled 3,000.  The combined surface area was found by adding all these areas together 2,500 + 3,000 + 1,500 was 7,000 square feet.  I checked my answer using a calculator and found the surface area of the rectangular prism would be 7,000 square feet.

Volume of a rectangular prism= Length x Width x Height

Volume = 50 x 25 x 30 =  37,500 cubic feet

The volume of the figure was found by using an equation.  I knew that the base of the figure was 50 by 25 feet.   So, I multiplied 50 times 25 to get 1,250 square feet.  The height of the rectangular prism was 30 feet, so I multiplied the base times the height to find out how much volume spans up the height of the prism.  I found that 1,250 times 30 was 37,500 cubic feet.  The volume of the rectangular prism is 37,500 cubic feet.