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Clare's recipe for banana bread won't fit in her favorite pan. The pan is 8 1/2 inches by 11 inches by 2 inches. The batter fills the pan to the very top, and when baking, the batter spills over the sides. To avoid spills, there should be about an inch between the top of the batter and the rim of the pan. Clare has another pan that is 9 inches by 9 inches by 2 1/2 inches. If she uses this pan, will the batter spill over during baking?

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Answer:

Solution

In order to find out how high the batter will be in the second pan, we must first find out the total volume of the batter that the recipe makes. We know that the recipe fills a pan that is 8.5 inch by 11 inch by 1.75 inches. We can calculate the volume of the batter multiplying the length, the width, and the height:

VV=8.5 in×11 in×1.75 in=163.625 in3

We know that the batter will have the same volume when we pour it into the new pan. When the batter is poured into the new pan, we know that the volume will be 9×9×h where h is the height of the batter in the pan. We already know that V=163.625 in3, so:

V163.625 in3163.625 in3163.625 in381 in22.02 in=l×w×h=9 in×9 in×h=81 in2×h=h≈h

Therefore, the batter will fill the second pan about 2 inches high. Since the pan is 3 inches high, there is nearly an inch between the top of the batter and the rim of the pan, so it will probably work for the banana bread (assuming that Leo is right that that an inch of space is enough).

Step-by-step explanation:

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Answer:

Nope

Step-by-step explanation:

The 1st equation is greater than the 2nd equation.

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