The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 60 feet on a side. What will be the volume of the new building in cubic feet?
Choose one: A) 3,937,500 cubic feet B) 6,619,898 cubic feet C) 11550√3 cubic feet D) 15,750√3 cubic feet E) 3,937,500√3 cubic feet
Volume of the Hexagon with side 200 and height 70 = Area * height   = 6*(sqrt(3)/4)(200^2)(70)   Volume of the center bull's eye that is similar in shape of a hexagon but side 60   = 6 * (sqrt(3)/4)(60^2)*70   Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(60^2)*70=6,619,898   Answer is 6,619,898 cubic feet
<result>B</result>
The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 60 feet on a side. What will be the volume of the new building in cubic feet?