Multiple choice

A cylindrical container of radius 6 cm and height 15 cm is fulled with ice-cream. The whole ice-cream has to be distributed to 10 children in equal cones with hemispherical tops. If the height of the conical portion is four times the radius of its base, find the radius of the ice-cream cone

  1. 3 cm

  2. 1 cm

  3. 4 cm

  4. 2 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The container volume is 540pi cubic centimetres, so each child's portion is 54pi cubic centimetres. A cone of radius r and height 4r plus a hemispherical top has volume 2pi r^3. Equating this to 54pi gives r^3 = 27, so r = 3 cm.

AI explanation

The total volume of ice cream is the volume of the cylinder, pi times 6 squared times 15, which is 540 pi cubic centimeters. The volume of one cone with a hemispherical top is one third times pi times radius cubed times 4 plus two thirds times pi times radius cubed, simplifying to 2 times pi times radius cubed. Dividing the total ice cream among 10 children means 2 times pi times radius cubed equals 54 pi, so radius cubed equals 27 and the radius is 3 cm.

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