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July 5th, 2016, 01:27 AM   #1
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Post How many door stops from a sphere ball?

My daughter asked for help, but I couldn't explain why the answer should be 44, and not 100, as I thought. Can you, please?

Given a sphere ball, diameter 400 mm.

How many door stops can be cut out of this ball? Door stops should be sized 5 cm x 10 cm x 15 cm.

My calculus went like this:
Let the doorstop be a kind of keg (pyramid shaped), with a bottom of 5 cm x 10 cm, and a length of 15 cm. The point of the pyramid pointing to the center of the sphere ball, the bottom of the pyramid would be at the outside of the ball.

Now the bottom of every pyramid is 5 cm x 10 cm = 50 cm ^2.

The surface of the ball is 4 pi r ^2, being 5024 cm ^2.

Dividing 5024 by 50, would make 100 door stops.

However, the answer in the book reads: 44. (without explaining)

Could you please explain how to get to this answer? My daughter will be happy with her father again
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July 5th, 2016, 02:18 AM   #2
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There is no mention of what the ball is made from, so we can melt it down.
There is no mention of the shape, so we assume a rectangular block

The volume of the sphere is 33510cm3
20*20*20*4*Pi/3

The volume of the door stops is 750cm3
5*10*15

You can therefore make 44 whole rectangular doorstops from the sphere.
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July 5th, 2016, 05:16 AM   #3
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Excellent and convincing calculation. Thank you, weirddave.

Now we have rectangular shapes, that we can't push under a door. But that is more of a real world problem, not a mathematical one. I think I'm not enough of a math man, then.
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July 5th, 2016, 06:59 AM   #4
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It depends what you call a door stop. A piece of wood screwed to the floor makes a good door stop, it stops damage to the wall if it is swung open.
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