Multiple choice

A cylindrical tank full of oil, with the ratio of its radius to its height being 7 : 4, is used to fill 24 identical cuboidal containers with dimensions 11 × 9 × 7. What is the sum of the radius and the height of the cylindrical tank?

  1. 22 units

  2. 28 units

  3. 33 units

  4. 42 units

  5. 48 units
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of 24 containers = 24 * 11 * 9 * 7 = 16632. Cylinder volume = pi * r^2 * h. Given r/h = 7/4, let r=7k, h=4k. Volume = pi * (49k^2) * (4k) = 196 * pi * k^3. Assuming pi=22/7, 196 * (22/7) * k^3 = 16632 -> 616 * k^3 = 16632 -> k^3 = 27 -> k=3. Radius = 21, height = 12. Sum = 33.

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