\fName Date MULTIVARIABLE CALCULUS FINAL PROJECT Summary: A sliceform is a three-dimensional shape assembled from flat slices that join together to form a grid structure. After researching sliceforms, your task is to create a template for a sliceform that represents a three-dimensional model that we have worked with this year (such as a cone, tetrahedron, hyperboloid, torus, hyperbolic paraboloid, ellipsoid, etc.). You will use this template to create a three- dimensional model of your sliceform and calculate its volume, mass, center of gravity, and centroid. For your convenience, given a three-dimensional solid G and a continuous density function S(x, y, z) : Mass of G: Center of Gravity (x, y, z) : Centroid (x, y, z) : M = [ S(x, y, z) dV x = fix . 8(x, y, z) dV x= _ fff xav G y =fff x . 8(x, y,z) dV y = SIS yay z= ]][ x . 8(x, y,z ) dV z = SIS zdv Requirements: You must... select a sliceform that no one else in the class has selected (this means, as a class, you will need to coordinate which student creates which model - use the Google Doc posted in Google Classroom to do this). locate and save a model picture of the solid you wish to recreate (for reference purposes). . create the sliceform template (do not make the template too small or it will be difficult to work with) define the three dimensional solid, G, you will use . write an equation for the density function, o(x, y, z) , you will use build your three-dimensional model of G calculate its volume calculate its mass locate the center of gravity locate the centroid