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HMMT 二月 2001 · CALC 赛 · 第 3 题

HMMT February 2001 — CALC Round — Problem 3

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. A balloon that blows up in the shape of a perfect cube is being blown up at a rate such that at time t fortnights, it has surface area 6 t square furlongs. At how many cubic furlongs per fortnight is the air being pumped in when the surface area is 144 square furlongs?
解析
  1. A balloon that blows up in the shape of a perfect cube is being blown up at a rate such that at time t fortnights, it has surface area 6 t square furlongs. At how many cubic furlongs per fortnight is the air being pumped in when the surface area is 144 square furlongs? 3 / 2 Solution: The surface area at time t is 6 t , so the volume is t . Hence the air is being √ √ 3 pumped in at a rate of t . When the surface area is 144, t = 24, so the answer is 3 6 . 2