# Volume of Revolution with Applet

- Author:
- Satvinder Singh

- Topic:
- Integral Calculus, Volume

## Investigate the Rotation of a Line about x-axis

## Q1.Investigate the Rotation using Spin slider, Enter y = 3 and Set a= -3 and b= 3.

Spin it up to 360 degrees. Which Solid shape is formed? What is the radius and height of that shape?

## Q1 a. Can you work out the volume of the Shape formed

What would be your procedure for Volume of the shape?

## Q2 a, Enter y = x+3, from a= -3 to b= 3, Spin it and move slider w

You may Untick the unhide rotation and disc boxes to see them clearly. Describe the Volume of the Shape formed?

## Q2b: y= x+3

When you rotate y = x+3 and you get the shape of the solid formed. Do you know the formula of volume of that Shape?

## Q3. Untick : Unhide the Rotation

The Red disc ( Circular shaped element), If you move slider w, what is changing with w?

## Q4. The Slider w is changing the radius of circular disc.

The Radius at different positions is actually given by the value of the function (y= f(x)) at different x values. So Remember radius of the Disc at 'x= w' would be f(w). if the width of the disc is 'dx' then what is the Volume of the Disc?

## Q5, Select the Correct option

as w is the variable, we can say the radius of the disc = f(x) ( at any value of x). and the width is dx. The Volume of the disc (Cylinder) would be

## Q6 if there are n- number of discs making a solid shape when you rotate a line or curve about x-axis from a to b

Then The Total Volume should be the sum of the volume of all discs and it is given by