Answer to Question #23224 in Mechanics | Relativity for Julietta Holguin

Question #23224
Your pancake recipe calls for 1.5 cups of flour to make 20 four-inch pancakes. But you want to make twelve eight-inch pancakes. How much flour should you use?
Expert's answer
Flour which needed to make one four-inch pancake:
1.5/20 = 0.075
We'll assume that the thickness of the pancakes with diameter four-inch and eight-inch are the same. A pancake is a cylinder. A cylinder with radius r and height h inch has a volume of V cubic inch given by
V = П*h*(r^2)
П = 3.14
V'/V = (r'^2)/(r^2) =(d'/2)^2/(d/2)^2 = (d'/d)^2
V', d' - volume and diameter of eight-inch pancake;
V, d - volume and diameter of four-inch pancake;
Flour which needed to make one eight-inch pancake:
( 0.075*V')/V =0.075* (d'/d)^2 = 0.075 * 4 = 0.3
Flour which needed to make twelve eight-inch pancake:
12 * 0.3 = 3.6
Answer: 3.6 cups of flour.

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