The region bounded by the given curve is rotated about the specified axis. find the volume v of the resulting solid by any method.
x2 + (y − 4)2 = 16; about the y-axis

The volume of the solid is a function of its definite integral.

The volume of the solid is:

The curve is given as:

Solve for x^2

Using the washer method, we have the following integral:

The graph passes through y = 0 and y = 8.

So, we have:

Substitute

Rewrite as:

Expand brackets

Open bracket

Evaluate like terms

Integrate

Expand

Simplify

Hence, the volume of the solid is:

Read more about volume of solids at:

link

Hence the volume of the solid is:

Step-by-step explanation:

We will use the washer method to compute the volume of the solid formed after rotating the given figure around y-axis as:

Clearly the resulting solid is a sphere.

Now the washer method is given as:

Volume=

Now we are given the equation as:

so we get the value of as:

Now the volume is computed as:

Volume=  

           =   from 0 to 8

Which is given by putting the limits.

Volume=  

Hence the volume of the solid is:

its 69.420

step-by-step explanation:

f is the midpoint of