Multiple choice

A hollow metallic cylindrical tank has an internal radius of 80 cm and height 200 cm. The thickness of the metal is 1 cm. If the tank is melted and cast into a right circular cone of height 3 m, find the radius of the cone, correct to two decimal places.

  1. 13.74 cm

  2. 17.94 cm

  3. 16.64 cm

  4. 15.34 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the hollow cylinder is pi * (R^2 - r^2) * h, where R=81 and r=80. Volume = pi * (81^2 - 80^2) * 200 = pi * 161 * 200 = 32200 * pi. Setting this equal to the cone volume (1/3) * pi * r_cone^2 * 300, we get r_cone^2 = 322, so r_cone = sqrt(322) approx 17.94.

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