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 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 ò -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 (ò dx) 9 - X2 , -3, 3 ) EXE
The result is 113.0973355 as predicted.
Press MENU.
F
ind 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 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 (ò dx) X, 0, 4 ) - F4 (ò 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)