SITE-C teams: Lesson 30

*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,

The volume of such a solid is the
volume of a sphere with radius 3. In other words, the volume is ^{4}/_{3}
p r^{3} where r = 3, i.e. 36p or 113.0973355. The volume of this solid can also be
expressed as a value of an integral, specifically, p ò _{-3 }^{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) **9 -** **X ^{2}**

The result is 113.0973355 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 Ö X*
*and press

Enter into the Y2 slot the expression 0.5 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) **F5** (ISCT) to get the first
point of intersection which is ( 0, 0). Press the right cursor arrow to get the second
point of intersection which is ( 4, 2 ).

Press **EXIT MENU 1 OPTN F4** (CALC) **F4** (ò
dx) **X, 0, 4 ) -** **F4** (ò dx) **0.25 X ^{2},
0, 4 ) EXE.**

The result is 2.666666667, so the volume of the desired solid is 2.666666667p or 8.37758041 cubic units.

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

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