Lainey Goodwin

2022-01-29

This scenrio has do around QUADRATICS problems.
You have been asked to bake the birthday cake of a little girl who is about to turn three. When looking up suggestions online on how to bake this cake, you found that most everyone suggests baking the cake in smaller circular cake pans that have a diameter of 6 inches. That’s the best way to get the height for the unicorn head. A normal circular cake pan (and the only kind you have) has a diameter of 9 inches. You need to buy cake pans. As an experienced baker, you know that the recipe you are planning on using usually fills two regular (9-inch) cake pans, with a little room to spare. How many 6-inch pans do you need to buy? (We’re going to assume that all cake pans are the same height.)

Roman Stevens

Expert

Step 1

Let the height of the 9-inch cake pan $=x.$
The formula to calculate the volume of a cake pan,$V=\pi {r}^{2}h,$ where h is the height of the pan.
Therefore, the volume of the 9-inch cake pan,$V=9x\pi .$
This implies the 9 inch cake pan can hold $9x\pi$ litres of cake batter.
Assume that all cake pans are the same height.
Then the height of the 6-inch cake pan $=x.$
The volume of the 6-inch cake pan,$V=6x\pi .$
This implies the 6 inch cake pan can hold $6x\pi .$ litres of cake batter.
Step 2
Given that the recipe fills two 9 inch cake pans.
Say, the recipe yields y litres of cake batter.
Then, $y=2\left(9x\pi \right)$
$\text{To finf the number of cake pans to be bought}$
Let the number of cake pans to be bought $=n$.
Then, we need to find n such that,
$y=n\left(6x\pi \right)$
$2\left(9x\pi \right)=n\left(6x\pi \right)$
$18x\pi =n\left(6x\pi \right)$
$n=\frac{18}{6}$
$n=3$
Therefore, the baker has to buy three 6-inch cake pans.

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