Problem 19 · 2021 Math Kangaroo
Hard
Algebra & Patterns
evaluate-formula
Show answer
Answer: E
Show hints
Hint 1 of 2
As paper is pulled off, the roll's diameter (the thickness y) shrinks.
Still stuck? Show hint 2 →
Hint 2 of 2
Relate the area of paper removed to x, then see how fast y changes as the roll thins.
Show solution
Approach: model how the roll's diameter shrinks with length pulled
- The unrolled length x is proportional to the paper area removed, which equals π(R² − ρ²) for current radius ρ.
- Since y = 2ρ, this gives y = 2√(R² − cx): y decreases and falls faster as the roll gets thin.
- That decreasing, downward-curving graph is E.
Mark:
· log in to save