Question
A rectangular cake has a length of 15 inches and a width of 15 inches. How many whole, square pieces of cake with side lengths of 2 1/2
inches can be cut from the cake?
inches can be cut from the cake?
Answers
GPT-4o mini
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 each square piece.
1. **Calculate the area of the cake:**
\[
\text{Area of cake} = \text{length} \times \text{width} = 15 \, \text{inches} \times 15 \, \text{inches} = 225 \, \text{square inches}
\]
2. **Calculate the area of one square piece of cake:**
\[
\text{Area of one square piece} = \text{side length} \times \text{side length} = 2.5 \, \text{inches} \times 2.5 \, \text{inches} = 6.25 \, \text{square inches}
\]
3. **Calculate how many square pieces can fit into the cake:**
\[
\text{Number of square pieces} = \frac{\text{Area of cake}}{\text{Area of one square piece}} = \frac{225 \, \text{square inches}}{6.25 \, \text{square inches}} = 36
\]
Thus, we can cut **36 whole square pieces** of cake with side lengths of 2.5 inches from the rectangular cake.
1. **Calculate the area of the cake:**
\[
\text{Area of cake} = \text{length} \times \text{width} = 15 \, \text{inches} \times 15 \, \text{inches} = 225 \, \text{square inches}
\]
2. **Calculate the area of one square piece of cake:**
\[
\text{Area of one square piece} = \text{side length} \times \text{side length} = 2.5 \, \text{inches} \times 2.5 \, \text{inches} = 6.25 \, \text{square inches}
\]
3. **Calculate how many square pieces can fit into the cake:**
\[
\text{Number of square pieces} = \frac{\text{Area of cake}}{\text{Area of one square piece}} = \frac{225 \, \text{square inches}}{6.25 \, \text{square inches}} = 36
\]
Thus, we can cut **36 whole square pieces** of cake with side lengths of 2.5 inches from the rectangular cake.