### Scribe for Monday

And g(x) = 2 + rt 4+4x-x^2

S is the region between f and g, write the interval that gives:

a) The volume generated by rotating s around the line y=5.

b) The Volume generated by rotating s around the line y=1.

c) The volume generated by rotating s around the y-axis.

Rotating two lines, It surface will be looks like a washer.

And the Volume of a cylinder V = pai (R^2-r^2)

a)---> pai

**S**(rt (4+4x-X^2) +2 -5) ^2 - (0.5X^2-2x+4-5)^2 dx

pai

**S**(rt(4+4x-x^2-3)^2-(0.5x^2-2x-1)^2 dx

b)---> pai

**S**(rt (4+4x-x^2)+3)^2-(0.5x^2-2x+5)^2 dx

c)---> Pai

**S**(3^2-y^(1/2)) dy

A roll of paper towels has dimesions

Find the volume of the papper

Volume of Pai r^2 h a cylinder

V = Pai h (R^2-r^2)

= pai h (R+h) (R-h)

**S (**2pai x) f(x) dx

(circle) (height) (width)

Nest scribe: steven :P