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sleepy545 · Feb 1, 2012, 10:34 PM

Can someone help with this math problem having a hard time figuring it out.

The sketch below shows a component which is stamped out of sheet steel. The square in the center has been discarded. These components are stamped out of a continuous steel coil with a width of 70cms. The stamping process requires a gap of 25mm between each component. The steel coil is supplied in lengths of 25 meters costing $200.

(Square inside of a circle) circle is 60cms and square is 30cms.

What is the approximate area of the remaining shape in square centimeters?

jcaron2 · Feb 6, 2012, 02:13 PM

First, find the total area of the shape. If I interpret what you said correctly, it sounds like that would be

$A=\pi*r^2-x^2=\pi*(0.3)^2-(0.3)^2$ ,

where r is the radius of the circle and x is the length of one side of the square (both in meters the way I wrote it).

Now figure out how many components can be stamped out of a coil: The shape itself is 60cm wide, and since a 25cm space is required between adjacent components, that means a component can be stamped every 85 cm. So how many times does 85cm go into 25m? A little over 29 times, so that means that you can get 29 shapes out of a single coil. That's a total area of 29A (where A is the area of one component, which you calculated above).

Finally, find the total area that the coil started with, and subtract the area of the 29 shapes. That's how much is left over.