SOLUTION TO PROBLEM R-9

Label the edges of the solid a, ar, and ar². Then

$$\mbox{Volume}= a (ar) (ar^2) = 8$$

and hence ar = 2. Also

$$\mbox{Surface Area}=2a^2r + 2 a^2r^2+2a^2r^3 = 32,$$

and hence

32=2(ar)(a+ar+ar²)=4(a+ar+ar²).

But this last expression is just the sum of the edge lengths.

Therefore the answer is 32.

Questions and/or comments should be directed to Judy Downey or Griff Elder

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Last modified:   Thu Mar 14 19:11:21 CST 2002