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Farhana has a cake recipe which states that the cake should be baked in a pan 8 inches in diameter. If farhana wants to use the recipe to make a cake of same depth but 12 inches in diameter,by what factor she should multiply the recipe ingredients?

Farhana has a cake recipe which states that the cake should be baked in a pan 8 inches in diameter. If farhana wants to use the recipe to make a cake of same depth but 12 inches in diameter,by what factor she should multiply the recipe ingredients? Correct Answer 2.25

Let the depth of the cake be h. Volume of the smaller cake, π r2 h = π (8/2)2 × h = 16πh Volume of the larger cake, π R2 h = π (12/2)2 × h = 36πh So, ingredients should be multiplied by (36πh / 16πh) = 2.25

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