Multiple choice

A cylinder of radius $6\ cm$ and height $h$ cm is filled with ice cream. The ice cream is then distributed among $10$ children in identical cones having hemispherical top. The radius of the base of the cone is $3\ cm$ and its height is $12\ cm$. Then the height $h$ of the cylinder must be

  1. $\dfrac{100}{7}\ cm$
  2. $18\ cm$
  3. $15\ cm$
  4. $\dfrac{200}{11}\ cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * 6^2 * h = 36 * pi * h. Volume of 10 cones = 10 * (1/3 * pi * 3^2 * 12 + 2/3 * pi * 3^3) = 10 * (36 * pi + 18 * pi) = 10 * 54 * pi = 540 * pi. 36 * pi * h = 540 * pi, so h = 540/36 = 15 cm.

AI explanation

The cylinder volume is pi times r squared times h, which equals pi times 6 squared times h, or 36 pi times h. The volume for one ice cream cone with a hemispherical top is one third times pi times 3 squared times 12 plus two thirds times pi times 3 cubed, totaling 54 pi. Multiplying by 10 children gives a required volume of 540 pi, so 36 pi times h equals 540 pi, meaning h equals 15 cm.

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