SITE-C teams: Lesson 29

*Use the* CASIO *CFX-9850G to find the
volume of the solid formed by rotating about the x-axis the region bounded by the x-axis,
y = x, x = 0, and x = 3.*

The volume of such a solid is the
volume of a cone with radius 3 and height 3. In other words, the volume is ^{1}/_{3}
p r^{2} h where r = 3 and h = 3, i.e. 9p or 28.27433388. The volume of this solid
can also be expressed as a value of an integral, specifically, p ò _{0
}^{3} y^{2} dx. Let’s verify this.

Turn on the **CASIO CFX-9850G** by pressing

Use the cursor arrows to highlight the RUN icon and press **EXE** or
just press **1** when at the main menu screen.

Press **SHIFT EXP** (p ) **x** **OPTN**
**F4** (CALC) **F4** (ò dx) **X ^{2}**

The result is 28.27433388 as predicted.

Press **MENU**.

Find the volume of the solid formed by rotating about the x-axis the region bounded by the x-axis, the function

Use the cursor arrows to highlight the GRAPH icon and press **EXE**
or just press **5** when at the main menu screen.

Enter into the Y1 slot the expression X* *and press

Press **SHIFT** **F3** (V-Window) **F1** (INIT), and set the y
parameters to:

Ymin = -2 |
Ymax = 6.2 |
Yscale = 1 |

Press **EXIT** to return to the function list, and press **F6**
(DRAW) to see the graph.

Press **SHIFT** **F5** (G-Solv) **F6** ( |> ) **F3** (ò dx), and press **EXE** to mark the lower bound of integration
which is x = 0.

Use the right cursor arrow to move to the point ( 4, 4 ), and press **EXE**
to mark the upper bound of integration and to compute the numerical integral. This is 8.

Thus the volume of the desired solid is 8p or 25.13274123 cubic units.

Press **EXIT**. Press **MENU**.

Turn off the **CASIO CFX-9850G** by pressing