Chapter 12.5, Problem 1BE

To determine

To RUN the program and make a graph that shows how the volume varies with $x$ and for what value of $x$ did you find the greatest volume.

Answer to Problem 1BE

  $x=2$

Explanation of Solution

Given:

The program is given in the textbook for finding the volume.

Calculation:

The following is the given BASIC program-

10 PRINT “X”, “VOLUME”

20 FOR X = 0 TO 3 STEP 0.25

30 LET $V=4/3*3.1459*X\uparrow 2*(3-X)$

40 PRINT X, V

50 NEXT X

60 END

Sample Output:

  $\begin{array}{l}X=0.25,V=0.72\\ X=0.5,V=2.627\\ X=0.75,V=5.3087\\ X=1,V=8.41\\ X=1.25,V=11.454\\ X=1.5,V=14.15655\\ X=1.75,V=16.05719\\ X=2,V=16.778\\ X=2.25,V=15.926\\ X=2.5,V=13.1079\\ X=2.75,V=7.9302\\ X=3,V=0\end{array}$

  

From the above graph it is clear that the maximum volume is when $x=2$