Letter to a Friend 4. The base of a tent is a regular hexagon with side length 8 feet. Three poles bent in the form of semicircles that lie in planes perpendicular to the base join pairs of opposite vertices. Cross-sections of the tent parallel to the base are regular hexagons with their vertices on the semicircular poles. (a) Find an expression with one term (ie. an integral) that gives the volume of the tent. (b) Evaluate the integral from part (a) to find a fully simplified expression for the volume. Check that this expression has the correct units. (c) What fraction of the volume of the surrounding hexagonal cylinder does the tent occupy