capacity of a cylinder

[rabbit8]

Can you help me out to see where I need to go from here on this problem?
A cylinder has one flat rectangular face that rests against a wall. The height of the cylinderis 30 feet and the face resting against the wall is 10 feet wide. If the wall is 5 feet from the center of the cylinder, what is the capacity of the cylinder in cubic feet?

I started out by trying to find the radius of the cylinder. I used pythagorean's theroy a^ + b^ = c^
I ended up with 5^ + 5^ = 50 for the radius, thus the diameter is 100

The circumference of the cylinder is 2pir or 2 x 3.14 x 50 = 314 Is this correct?
I am unsure if I am going about solving this problem the correct way. How do I figure out how much of the cylinder is not being used becuase of the part that is against the wall?
Thanks

 

[TchrWill]

Can you help me out to see where I need to go from here on this problem?
A cylinder has one flat rectangular face that rests against a wall. The height of the cylinderis 30 feet and the face resting against the wall is 10 feet wide. If the wall is 5 feet from the center of the cylinder, what is the capacity of the cylinder in cubic feet?

I started out by trying to find the radius of the cylinder. I used pythagorean's theroy a^ + b^ = c^
I ended up with 5^ + 5^ = 50 for the radius, thus the diameter is 100

The circumference of the cylinder is 2pir or 2 x 3.14 x 50 = 314 Is this correct?
I am unsure if I am going about solving this problem the correct way. How do I figure out how much of the cylinder is not being used becuase of the part that is against the wall?
Thanks

Draw yourself a picture.
You should immediately see that the radii are at angles of arctan(5/10) =26.565º to the diameter.
You now have the capability of determining the cross sectional area of the cylinder.
Having that, the volume is the cross sectional area times the height.

Let us know how you make out.

 

[soroban]

Hello, rabbit8!

A cylinder has one flat rectangular face that rests against a wall.
The height of the cylinder is 30 feet
The face resting against the wall is 10 feet wide.
The wall is 5 feet from the center of the cylinder.
What is the volume of the cylinder in cubic feet?

Your work is a bit off . . .

This is the base of the cylinder.

              * * *
          *           *
        *               *
       *          r   * |
                    *   |5
      *           *     |
      *         * - - - *
      *           *  5  |
                    *   |5
       *              * |
        *               *
          *           *
              * * *

\(\displaystyle \text{Pythagorus says: }\;5^2+5^2 \:=\:r^2 \quad\Rightarrow\quad r \:=\:\sqrt{50} \:=\:5\sqrt{2}\text{ ft}\)

\(\displaystyle \text{The area of the entire circular base is: }\:\pi r^2 \:=\:\pi(5\sqrt{2})^2 \:=\:50\pi \text{ ft}^2\)

\(\displaystyle \text{The area of the base of the cylinder is: }\:\tfrac{3}{4}\times 50\pi \:=\:37.5\pi\text{ ft}^2\)


\(\displaystyle \text{Therefore, the volume is: }\;V \;=\;A\cdot h \:=\37.5\pi)(30) \;=\;1125\pi \text{ ft}^3\)