Multiple choice

A balloon is in the form of right circular cylinder of radius $1.5\ m$ and length $4\ m$ and is surmounted by hemispherical ends. If the radius is increased by $0.01\ m$ and the length by $0.05\ m$, the percentage change in the volume of the balloon is

  1. $2.38\%$
  2. $2.48\%$
  3. $2.038\%$
  4. $2.58\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

The balloon's total volume is the sum of the cylindrical part's volume and the volumes of the two hemispherical ends, which equals pi * r^2 * h + (4/3) * pi * r^3. Substituting r = 1.5 and h = 4 gives an initial volume of 9pi + 4.5pi = 13.5pi cubic meters. Using the new dimensions r = 1.51 and h = 4.05, the new volume is pi * (1.51)^2 * 4.05 + (4/3) * pi * (1.51)^3, which equals 13.8348pi cubic meters. The percentage increase is calculated as ((13.8348pi - 13.5pi) / 13.5pi) * 100, yielding 2.48%.

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