SITE-C teams: Lesson 28

*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 = 2, x = 0, and x = 3.*

The volume of such a solid is the
volume of a cylinder with radius 2 and height 3. In other words, the volume is p r^{2}
h where r = 2 and h = 3, i.e. 12p or 37.69911184. 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) **2 ^{2}**

The result is 37.69911184 as predicted.

Press **MENU**.

Find the volume of the solid
formed by rotating about the x-axis the region bounded by the x-axis and the function f(x)
= 6 + x - x^{2}.

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 6 + X - X^{2}* *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) **F1** ( ROOT ) to obtain the
first root which is ( -2, 0).

Press the right cursor arrow to obtain the second root which is ( 3, 0 ).

Press **EXIT MENU 1 OPTN F4** (CALC) **F4** (ò
dx) **(** **6 + X - X ^{2 })^{2}, -2, 3 ) EXE.**

Thus the volume of the desired solid is 104.1667p or 327.2493395 cubic units.

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

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