Find the volume of the resulting solid Questions

[killasnake]

Hi, I really do not know how to do these problems. Could someone help.

A ball of radius 12 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.

_____________

and

Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by

\(\displaystyle y=x^2\)

\(\displaystyle y=3x\)

about the x-axis.

____________

 

[Unco]

Some steps you may like to follow, killasnake:

1. Draw a diagram, ie. the appropriate graphs and shade in the desired region. For the first problem, consider \(\displaystyle \mbox{y = \sqrt{12^2 - x^2}\) and \(\displaystyle \mbox{y = 8}\).

2. Using the washers method, determine the area of a washer at some value of x. For the first problem this will be \(\displaystyle \pi(12^2 - x^2) - \pi(8^2)\).

3. The volume is then given by the integral of this area with respect to x with appropriate limits. For the first problem, Pythagoras is required to establish the outer limit.

See how you go and show us your efforts.