Question

Due in 4 hours, 25 minutes. Due Wed 06/20/2018 11:55 pm A volume is described as follow 1. the base is the region bounded by y 2- and y -0 2. every cross section parallel to the x-axis is a triangle whose height and base are equal. Find the volume of this object. volume S: Preview Get help: Video License Points possible: 1 This is attempt 1 of 5. Submit

Answer 1

We know that, ifthe cross section is parallel to the a-aris andits area is function of y.say A(y) then the volumn ofthe solid on [c,d is given by: V-] A(y) dy From the graph we can see that they-intercept is (c,d)-(0,2) To determine the area A(y) which gives the area of any cross section oftriangle whose base is equal to the beight. Let's consider a segment AB which is parallel to r-axis. Notice that this segment is the base of any cross-section triangle. Let's begin with the equation and write as a value ofa. Now, look at the segment and we can easily say that the r-cordinate to the right is 16-8y and to the left is -16-8y Length of segment and base of any tangle=2/T and height-base 2/16-8y = 2(16-8y)=32-16y :. Volume(V)(32-16y)dy 32-s(64-32)-32 umits