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, fraction30a.gif (1818 bytes)

The volume of such a solid is the volume of a sphere with radius 3. In other words, the volume is 4/3 p r3 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 -3 3 y2 dx. Let’s verify this.

Turn on the CASIO CFX-9850G by pressing AC/ON.

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 ( dx) 9 - X2 , -3, 3 ) EXE

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 fraction30b.gif (2047 bytes)

 

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 EXE to store it in memory.

Enter into the Y2 slot the expression 0.5 X and press EXE to store it in memory.

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 ( dx) X, 0, 4 ) - F4 ( dx) 0.25 X2, 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 SHIFT AC/ON (OFF)