You are helping design a four-sided dreidel that will be made out of clay.[br]Before construction begins, you must determine how much clay is needed for the body of the dreidel, based on the mass of the finished product. The body has a height of 6 cm, and is centered on the z-axis. The cross sections of the body perpendicular to the z-axis are squares with side lengths [math]L\left(z\right)=\frac{2z}{3}\left(1-\frac{z}{6}\right).[/math]The design of the dreidel ensures that it will only spin when constructed properly, with the correct volume and mass. [br]The density of the clay is given by the function [math]\delta\left(x,y,z\right)=1+0.2z[/math] grams per cubic centimeter.[br][br]Compute the mass of the needed clay. If you enter the correct mass below, you will be able to spin the dreidel.