A certain cake recipe states that the cake should be bake in a pan 8 inches in diameter. Of jules wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should he multiply the recipe ingredients

Area factor is in question here!

The factor is area of cake with 12 inches diameter divide by area of cake with 8 inches diameter

Area = Pi times radius squared

For cake with 12 inches diameter, the area = Pi times 6^2

For cake with 8 inches diameter, area = Pi times 4^2

Area factor = (Pi times 36) / (Pi times 16) = 36/16 = 2.25

He should multiply the recipe ingredients by 2.25