Aball of radius 15 has a round hole of radius 5 drilled through its center. find the volume of the resulting solid. hint: the upper half of the ball can be formed by revolving the region bounded by the curves y.

The volume of the ball with the drilled hole is:

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

Then we set the integral for the volume by using shell method:

That can be solved by substitution:

The limits of integration also change:

For x=5:

For x=15:

So the integral becomes:

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

Then applying the basic rule we get:

Since that is just half of the solid, we multiply by 2 to get the complete volume:

range is infinite on both x and y axis positive and negative

step-by-step explanation:

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step-by-step explanation: