http://www.youtube.com/watch?v=0PADeY4GVmo&feature=related

How to store grain?

Lets explore some possible containers

15 minutes

Once you have decided on a container.

You need to measure how much grain it can

hold.

Share Ideas: Pros and cons

Hoppers

What do you have?

Generalising

Going into business as a hopper designer.

Class effort

Farmer Doyle has the cuboid section of his hopper which holds 125m3 of wheat. He wants to add this funnel section to the cuboid section.

How much wheat will the total hopper hold?

Ignoring the small how at the bottom that allowing an opening

166.7m3

Going into business as a hopper designer.

1) This hopper is waiting in the warehouse to be sold.

a) What is the volume of the hopper?b) The price of this hopper is £15 for

every m2 of grain the hopper can contain how much should this hopper be sold for?

2) a) What is the clearance of the hopper outlet to the ground?

b) The hopper has a width of 12m. The cuboid section can how 1800m3 of flour, what amount of the flour can the hopper hold in total?

1a) 249.6m3

b) £3744

2a) 3mb) 2052m3

Going into business as a hopper designer.

• Farmer Giles wants the pyramid section of his square based hopper to hold 561cm3 what dimensions could the hopper be?

• Flo the flour farmer wants her hopper to be no taller than 20metres so that it is not taller than her barn but she needs it to hold 895m3. what dimensions could the hopper be?

What mathematics have we used?What skills have you practised?

What do you think where the intended learning objectives?

Intended objectives:

• To design different nets• To calculate volume of simple shapes• To calculate volume of complex shapes• To use formula• To create formula• To solve complex geometrical problems• To use trial and error• To consider functionality and apply mathematics

to real life problems.

• Can we gernalise that?• We know how to generalise for the volume of

cuboids.• Lets explore the a prism shape.

• You have done so well in inventing a gernal formula, a company is willing to pay to desgn hoppers,

Rough lesson plan.• Introduce idea of a hopper. • How to find its volume. Why is it pointed?? Why do we need to know

it volume????• Splitting it up into lots of trapezoidal prisms. The smaller the trapezium

the more accurate we can be.

• Can we generalise this........... Not really......why would we need to generalise???

• New approach we know how to calculate the volume of a cuboids how does that compare to a pyramid. (or cylinder and cone) experiment trial and error. Compare the formula. Can we generalise. ..........

Tank Connection Liquid Hopper Bottom Storage Capacity

Calculator PROGRAM INPUT

English Metric

Diameter: ft m

Eave Height: ft m

Hopper: °

Outlet: in cm

Outlet Length: in cm

Clearance: ft m

Freeboard: in cm

154.5740.312.28451230.481230.482.50.7622.50.762CalculatetrueLiquid Hoptankcalcapimages/smTank Conn

Mechanical partsA general term for a chute with additional width and depth for temporary storageHopper (particulate collection container), a large container used for dust collectionPart of a combine harvesterA storage container used to dispense granular materials through the use of gravity, sometimes assisted by mechanical agitation, an example is a paintball loader

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