Multiple choice

A hollow metallic cylindrical tube has an internal radius of $3cm$ and height $21cm$. The thickness of the metal is $0.5cm$. The tube is melted and cast into a right circular cone of height $7cm$. Find the radius of the cone, correct to one decimal place.

  1. $6.4cm$
  2. $5.4cm$
  3. $1.4cm$
  4. $3.4cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of tube = pi * (R^2 - r^2) * h = pi * (3.5^2 - 3^2) * 21 = pi * (12.25 - 9) * 21 = pi * 3.25 * 21 = 68.25 * pi. Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * r^2 * 7. Setting them equal: 68.25 = (7/3) * r^2. r^2 = 68.25 * 3 / 7 = 29.25. r = sqrt(29.25) approx 5.4.

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