1951 AHSME Problems/Problem 23
Problem
The radius of a cylindrical box is inches and the height is inches. The number of inches that may be added to either the radius or the height to give the same nonzero increase in volume is:
Solution
Let be the number of inches increased. We can set up an equation for :
Expanding gives .
Combining like terms gives the quadratic
Factoring out an gives .
So either , or .
The first equation is not possible, because the problem states that the value has to be non-zero. The second equation gives the answer, Thus the answer is .
See Also
1951 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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