# How do you find the surface area generated when the curve #y=sqrt(r^2-x^2), 0<=x<=a# is rotated about the x axis?

##### 2 Answers

Take a piece of the curve whose length is the differential of arc length

The surface area of the corresponding piece of the solid is

the circumference of revolution time the differential of arc length

which is

#2pif(x)sqrt(1+(f'(x))^2) dx#

Using just the values

# = 2pi int_0^a r dx#

# = 2pi r a#

Apr 17, 2018

#### Explanation:

The formular is