Imagine a hexagonal building with base , side and roof as hexagon
Sum of angle of hexagon = 180(n-2) where n is number of side
= 180(6-2)=720
Each angle will be 720/number of sides = 720/6=120
Now imagine the base of building with six sides. You can form 6 triangle all converging at the center of hexagon. These 6 triangle each will be equilateral triangle with side 200 feet as that is the side of base of hexagon.
Area of 1 such equilateral triangle = \(\sqrt{3} / 4 * (side)^2\)
=\(\sqrt{3}/ 4 * (200)^2 = 10,000 \sqrt{3}\)
Area of 6 such triangle will be= \(6*10,000 \sqrt{3}= 60,000\sqrt{3}\)
Now we know area of base of hexagon. To find volume we need third dimension which is height
Hence volume of complete hexagon = area of hexagon * height
= \(60,000\sqrt{3} * 70 = 4,200,000\sqrt{3}\)
Now there is hexagon bull's eye cut out right through the building.
Proceeding in similar fashion to find out the volume of this hexagonal bull's eye
Volume of hexagon bull's eye = area of hexagonal bull's eye * height
= (area of 6 triangle with base 50) * height
=\(3750 \sqrt{3}* 70 =262500\sqrt{3}\)
Hence volume of new building= volume of complete building - volume of bull's eye
= \(4,200,000\sqrt{3}-262500\sqrt{3}\)
= \(3,937,500\sqrt{3}\)
OA E.
On a slightly different note, with 14 million unemployed, last thing Defense Department needs is new building.
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My dad once said to me: Son, nothing succeeds like success.