Problem: The radius Rβ of a cylindrical box is 8 inches, the height H, is 3 inches. The volume V=ΟR2H is to be increased by the same fixed positive amount when Rβ is increased by xβ inches as when Hβ is increased by xβ inches. This condition is satisfied by:
Answer Choices:
A. no real value of x
B. one integral value of x
C. one rational, but not integral, value of x
D. one irrational value of x
E. two real values of x
Solution:
V=ΟR2H,Ο(R+x)2H=ΟR2(H+x)
R2H+2RxH+x2H=R2H+R2x
2Rxh+x2H=R2x
since xξ =02RH+xH=R2,x=HP2β2RHβ
For R=8,H=3x=316β, so that (C) is the correct choice.