The base of a tent is a regular hexagon of side length 3 feet. Flexible poles extend between each pair of opposite vertices in semi-circular arcs perpendicular to the ground. Cross sections of the tent parallel to the ground are all regular hexagons. Tent: Top View of the base: 3 ft Cross-section Angled View: Cross-section Side View: 1. Show how to find the area of a hexagon where the distance from one vertex to the opposite vertex is D. 2. Place the cross-sectional side view on an xy axis as shown above. Write a function describing the curve of the semi-circular pole, then find the volume of the hexagonal cross section at a height of y_i. 3. Find the volume of this tent by stacking hexagonal cross sections from the ground up.Place a line segment of fixed length L units in the first quadrant of the xy-plane with one endpoint at the origin, at an angle of & measured from the x-axis. Revolve this line segment about the y-axis to create a cone-shaped cup. X 1. Sketch a picture of this line segment in the plane. Sketch a picture of a cup where O is large and sketch a picture of a cup when O is small. 2. Use the techniques associated with solids of revolution to compute the volume of such a cone. Your limits of integration should depend on the variable O. 3. Find & that maximizes the volume of this cone, then find that volume. 4. What is the height of the water level when the glass (with ( from #3) is half-full