To determine how many whole square pieces of cake with side lengths of 2.5 inches can be cut from a rectangular cake with dimensions 15 inches by 15 inches, we first need to calculate the area of the cake and the area of one square piece of cake.
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Calculate the area of the rectangular cake: \[ \text{Area of the cake} = \text{length} \times \text{width} = 15 , \text{inches} \times 15 , \text{inches} = 225 , \text{square inches} \]
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Calculate the area of one square piece of cake: \[ \text{Area of one square piece} = \text{side} \times \text{side} = 2.5 , \text{inches} \times 2.5 , \text{inches} = 6.25 , \text{square inches} \]
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Determine how many whole pieces can be cut: To find the number of whole square pieces we can cut from the cake, divide the area of the cake by the area of one square piece: \[ \text{Number of pieces} = \frac{\text{Area of the cake}}{\text{Area of one square piece}} = \frac{225}{6.25} \]
Now, perform the division: \[ \frac{225}{6.25} = 36 \]
Therefore, the number of whole square pieces of cake that can be cut from the rectangular cake is 36.
The correct answer is C. 36.