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 r2 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 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) 22 , 0, 3 ) EXE

The result is 37.69911184 as predicted.

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 - x2.

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 - X2 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) 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 - X2 )2, -2, 3 ) EXE.

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