SITE-C teams: Lesson 29

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 = x, x = 0, and x = 3.

The volume of such a solid is the volume of a cone with radius 3 and height 3. In other words, the volume is 1/3 p r2 h where r = 3 and h = 3, i.e. 9p or 28.27433388. 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) X2 , 0, 3 ) EXE

The result is 28.27433388 as predicted.

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 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) F6 ( |> ) F3 (ò dx), and press EXE to mark the lower bound of integration which is x = 0.

Use the right cursor arrow to move to the point ( 4, 4 ), and press EXE to mark the upper bound of integration and to compute the numerical integral. This is 8.

Thus the volume of the desired solid is 8p or 25.13274123 cubic units.