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 35 feet on a side. What will be the volume of the new building in cubic feet?  Select the correct option
A) 3,937,500 cubic feet	B) 15,750 cubic feet	C) 11550√3 cubic feet	D) 15,750√3 cubic feet	E) 7,051,828 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 35   = 6 * (sqrt(3)/4)(35^2)*70   Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(35^2)*70=7,051,828 cubic feet   Answer is 7,051,828 cubic feet
<result>E</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 35 feet on a side. What will be the volume of the new building in cubic feet?