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A plastic funnel is used to pour liquids through narrow apertures. Have you ever tried pouring a drink from a glass back into a bottle ? If we imagine a funnel as a complete cone (why isn't it?), what shape cone would use the least amount of plastic to manufacture a funnel containing a set volume?
You don't need a specified volume, but it may help to ask what proportion cone would hold a litre of liquid using the least amount of plastic. See the Hint for more help. |
The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?
What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?