Cross Sectional Area

Cross Sectional Area Name ______

Use the following shapes and calculate the Volume of the figure assuming the cross- section has the given shapes.

For problems 1,2, the cross-sections are

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.

a) Find the volume if each cross-section is a square.

b) Find the volume if each cross-section is a equilateral triangle.

c) Find the volume if each cross-section is a semi-circle

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.

b) Find the volume if each cross-section is a equilateral triangle.

c) Find the volume if each cross-section is a semi-circle

3) Given the following functions and sketch, answer these questions 1 f( x ) = g( x )= 5 - x x

a) Find the Area of region R.

b) Rotate the region about the x-axis. Find the volume

c) Rotate the region about the y-axis. Find the volume

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.