Choose region 2 from the Explore & Test page that is bounded by the curves y = (x − 3)2 when x ≥ 3, x = 0, y = 4. Set the axis of revolution to be the y-axis and use the first slider to rotate the region around the y-axis. The solid generated resembles a coffee cup without a handle. Move the second slider to see how the volume of the disks can be used to approximate the volume of the coffee cup.

V= 76 π cubic units

Step-by-step explanation:

y= ----->

Here we will apply the risk method.

Risk method: consider a strip of length x and width dy as

a) Radius= R(y) = x =

[We rotate this disc about y-axis to get a disk]

b) Cross-section area = A(y)= π

                                    = A(y)= π (y+9+6 )

--------> Volume of the disc = A(y) x dy

c) Required volume= v = A(y) x d(y)

                         V=  π (y + 9 + 6 ) dy

                         V=  π [

                          V= 76  π cubic units.

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step-by-step explanation: