geometry question

Question

The Muffin Man's most popular item is Gingy, the gingerbread man, which has a height of 6 in. He wants to make a larger version with double the height. If a single 6 in. Gingy requires 25 grams of dough and the gingerbread men are Similar Solids, how much dough would be required to make the new larger gingerbread man?

Answer 1

So Jackie M.,

The concept here is scaling vs. number of dimensions scaled!

If you double the length of a line segment, it's just 2x as long.

If you double the dimensions of an infinitely-flat square, it has 2x2 = 4 times the area

If you double the dimensions of a solid (in 3-D), it has 2x2x2 = 8 times the volume.

We will assume that the similar solid gingerbread cookies are cooked to the same texture (density), that is, neither is puffier than the other. Then the bigger cookie takes 25x8=200g dough.

Now comes the fun part! Should she cook the larger cookies for twice as long, because they are twice as thick? If I were her, I would do a trial run, before I burn up all my cookie dough!

Hint: If you are doing loaves of hand-made bread: bake in the oven until the upper crust taps with a hollow sound, then flip the loaf over in a microwave and cook by minutes until the steam stops evolving from the former underside. Microwave is very efficient for delivering heat into the top surface of food, but that wouldn't work for cookies, which require browning and a slight amount of crisping.

-- Cheers, --Mr. d.

Answer 2

If the heights are ratio of 1:2, then the volumes would be in the ratio of 1:2^3 = 1:8 So if 25g is required to make smaller gingerbread man, then 25g * 8 = 200g is required to make bigger one.