Disk problem and frustum

[jman2807]

I have these two calculus problem and I don't really have any clue where to start

1. Find the volume of the described solid S.

The base of S is a circular disk with radius r. Parallel cross-sections, perpendicular to the base, are squares.

Also I have this problem...

2. Find the volume of the described solid S. Use only the variables h, R, and r in your answer.

I have the following definition:

"A frustum of a right circular cone with height h, lower base radius R, and top radius r."

I was able to get the answer but not using calculus. My teacher said something about finding the equation of the line from R to r. I found what I thought would be the equation but am lost from there.

Thanks for the help in advance.

 

[stapel]

I found what I thought would be the equation but am lost from there.

What equation did you get?

Thank you.

Eliz.

 

[jman2807]

Nevermind on the second one, I got it, however i still have no clue on the first.

 

[skeeter]

equation for the circle is \(\displaystyle x^2 + y^2 = r^2\)

one representative "slice" of volume taken perpendicular to the x-axis is \(\displaystyle dV = (2y)^2 dx = 4y^2 dx\)

since \(\displaystyle x^2 + y^2 = r^2\), \(\displaystyle y^2 = r^2 - x^2\)

so ...

\(\displaystyle dV = 4(r^2 - x^2)dx\)

integrate the last expression from -r to r, or use symmetry and double the result while integrating from 0 to r.

\(\displaystyle \L V = 2 \int_0^r 4(r^2 - x^2) dx\)

 

[jman2807]

Got it, Thanks