1960 AHSME Problems/Problem 23
Problem
The radius of a cylindrical box is inches, the height is inches. The volume is to be increased by the same fixed positive amount when is increased by inches as when is increased by inches. This condition is satisfied by:
Solution
Since increasing the height by inches should result in the same volume as increasing the radius by inches, write an equation with the two cylinders (one with height increased, one with radius increased). By the Zero-Product Property, or . However, since must be increased, discard as a possible value. Thus, the length should be increased by inches, so the answer is .
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
All AHSME Problems and Solutions |