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Answer :
To determine which cake offers more for the money, calculate the volume of both the rectangular and round cakes. The rectangular cake has a larger volume.
The question is asking us to compare the volumes of a 9" by 13" rectangular cake with that of an 8" diameter round cake that is twice as tall as the rectangular cake to determine which gives more cake for the money.
First, calculate the volume of the rectangular cake:
- Rectangular Cake Volume = Length × Width × Height
Assuming we were given the height of the rectangular cake or it can be defined through another piece of information:
- For example, if the height is 2 inches (instead of variable, take number), then the volume would be 9" × 13" × 2" = 234 cubic inches.
Next, calculate the volume of the round cake:
- Round Cake Volume = π (Diameter/2)²× Height
Since the round cake is twice the height of the rectangular cake:
- Let's say the height of the round cake is 4 inches (twice the rectangular cake's height if it was 2 inches). The volume is π × (8"/2)² × 4" = π × 16 × 4 = 201.06 cubic inches (considering π ≈ 3.14159).
Therefore, the rectangular cake offers a larger volume and thus more cake for the money.
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Final answer:
To compare which cake offers more value for money, we calculate the volume of each using appropriate formulas. It's found that the rectangular cake gives more volume, and therefore more cake, for the same price.
Explanation:
To solve this problem, you need to determine the volume of each cake, using the formulas for the volume of a rectangular prism and a cylinder respectively. These are given by volume = length x width x height for the rectangular cake, and volume = pi x (diameter/2)^2 x height for the round cake.
First, calculate the volume of the rectangular cake. Using the provided dimensions, we have: volume = 9" x 13" x h = 117h cubic inches.
For the round cake, the diameter is 8", so the radius is 4". It's also given that this cake is twice the height of the rectangular cake, so we can denote it as 2h. Volume becomes: volume = pi x (4)^2 x 2h≈ 100.48h cubic inches.
From these calculations, we can see that for the same height, the rectangular cake has more volume and therefore more cake for the money, at 117h cubic inches versus the round cake's 100.48h cubic inches.
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