This scenrio has do around QUADRATICS problems. You have been asked to bake the birthday...

Step 1
$\text{Volume of}9-inch\text{cake pan:}$
Let the height of the 9-inch cake pan $=x.$
The formula to calculate the volume of a cake pan,${\displaystyle V=\pi r^{2}h,}$ where h is the height of the pan.
Therefore, the volume of the 9-inch cake pan,${\displaystyle V=9x\pi .}$
This implies the 9 inch cake pan can hold $9x\pi$ litres of cake batter. $\text{Volume of}6-inch\text{cake pan}$
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,${\displaystyle V=6x\pi .}$
This implies the 6 inch cake pan can hold ${\displaystyle 6x\pi .}$ 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, ${\displaystyle y=2\left(9x\pi \right)}$
$\text{To finf the number of cake pans to be bought}$
Let the number of cake pans to be bought $=n$.
Then, we need to find n such that,
${\displaystyle y=n\left(6x\pi \right)}$
${\displaystyle 2\left(9x\pi \right)=n\left(6x\pi \right)}$
${\displaystyle 18x\pi =n\left(6x\pi \right)}$
${\displaystyle n=\frac{18}{6}}$
$n=3$
Therefore, the baker has to buy three 6-inch cake pans.