Quizzes & Puzzles1 min ago
Problem!
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Sugar is leaking out of a container in a cone pile on the floor.Italways has a base width of 1.8x theheight. If theradius of the pile is increase at rate of 2.5cm/when the base radius is 80cm, at what rate is the sugar leaking out of the container.?
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Well done, bobbin. I haven't checked your working but if Etch says you're in the right ball park you must have understood the method (I think Etch is probably better at maths than me).
The volume of a cone isn't one of the commonly-known formulae but, now that you know it, can you solve this puzzle?
A cylindrical cheese weighs 3 LB. A customer at the shop wants 1LB of cheese and the shopkeeper has only a cheese-wire (no other means of measuring). How can he cut a piece weighing exactly 1LB?
The volume of a cone isn't one of the commonly-known formulae but, now that you know it, can you solve this puzzle?
A cylindrical cheese weighs 3 LB. A customer at the shop wants 1LB of cheese and the shopkeeper has only a cheese-wire (no other means of measuring). How can he cut a piece weighing exactly 1LB?
OK. bhg481's method over-estimates the mathematically calculated flow rate by just over 3%. Incidentally, when I said earlier that "the rate of increase of the volume of the cone is not linearly dependent on the rate of change of the radius of the cone base" that was incorrect. The rate of increase of the volume of the cone IS linearly related to the rate of change of the radius of the cone base: for a given size of cone, doubling the rate of increase of the volume would double the rate of change of the radius. What I should have said is that, for a given rate of change of volume, the rate of change of the radius of the cone base is not linear with respect to the radius of the cone base: as the base radius gets larger, the rate of change of radius will reduce, hence the difference in bhg481's method.
