<p>Cross Sectional Area Name ______</p><p>Use the following shapes and calculate the Volume of the figure assuming the cross- section has the given shapes. </p><p>For problems 1,2, the cross-sections are </p><p>1) A 3 dimensional figure has a base made up of the intersections of the following equations. f( x )= x , g( x) = 0 , x = 9 . Find the volume of the following figures.</p><p> a) Find the volume if each cross-section is a square.</p><p> b) Find the volume if each cross-section is a equilateral triangle.</p><p> c) Find the volume if each cross-section is a semi-circle</p><p> x 2 y 2 2) A 3 dimensional figure has an elliptical base with the equation + = 1 4 9 a) Find the volume if each cross-section is a square.</p><p> b) Find the volume if each cross-section is a equilateral triangle.</p><p> c) Find the volume if each cross-section is a semi-circle</p><p>3) Given the following functions and sketch, answer these questions 1 f( x ) = g( x )= 5 - x x</p><p> a) Find the Area of region R.</p><p> b) Rotate the region about the x-axis. Find the volume</p><p> c) Rotate the region about the y-axis. Find the volume</p><p> d) If the region was the base to a 3 dimensional figure with a cross section that formed equilateral triangles when sliced perpendicular to the x-axis, find the R volume.</p>