Calculus

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1. Chris makes an open-topped box from a 30-cm by 30-cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square to the nearest hundredth of a centimetre, so that the volume of the resulting box is more than 100cm(cubic)?

2.A cylindrical vat must hold 5m(cubic) of liquid cake mix. The vat must be wider than it is tall, but no more than 3m in diameter. What dimensions will use the least amount of material?

The flap square is the height of the box.

Volume= (30-2h)^2 * h check that with a sketch.

max volume..
dV/dh= 2(30-2h)(-2h)+ (30-2h)^2=0
or 4h=30-2h or h=5
so check that to see if volume is greater than 100..

On the second, write the volume and surface area equations, then minimize surface area.

Thanks, I'll give it a try.

  • Calculus -

    cool^2

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