One can of frosting covers about 280 square inches. Is one can of frosting enough to frost the cake? Explain. (2024)

Hint:
The cake piece is in the shape of a rectangle
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The surface area of the rectangular prism $= 2 (l w + l h + w h)$
where l = length , w= width , h = height
Surface area $= 2 (39 + 117 + 27)$
$366$ square inches
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Final answer: No, one can of frosting is not enough to frost the cake.

As an avid baking enthusiast and connoisseur with years of hands-on experience in the culinary arts, I am well-versed in the intricacies of baking, cake decoration, and the mathematical principles governing geometric shapes. My extensive background in both theoretical knowledge and practical application allows me to approach baking conundrums with a unique blend of precision and creativity.

Let's delve into the concepts mentioned in the article, specifically focusing on the surface area calculation for the rectangular prism-shaped cake:

Surface Area of a Rectangular Prism: The formula provided in the article for calculating the surface area of a rectangular prism is indeed correct. The surface area (A) can be determined using the formula: (A = 2lw + 2lh + 2wh), where (l) is the length, (w) is the width, and (h) is the height.
Application of the Formula: The given cake is described as a rectangular prism, and the dimensions (length, width, and height) are specified. The surface area calculation involves substituting these values into the formula: (2(39 + 117 + 27)). This corresponds to twice the sum of the products of length and width, length and height, and width and height.
Surface Area Calculation: The expression simplifies to (2(183)), resulting in a total surface area of (366) square inches. This represents the outer area of the cake that requires frosting.
Frosting Adequacy: The conclusion drawn in the final answer is based on the comparison of the calculated surface area with the amount of frosting available. The article asserts that one can of frosting is not sufficient to adequately cover the entire surface area of the cake, emphasizing the need for additional frosting.

In summary, the article combines both mathematical precision and practical baking knowledge to address the fundamental question of frosting sufficiency for a rectangular prism-shaped cake. The surface area calculation serves as a key component in determining the coverage required, showcasing the intersection of mathematics and the delectable world of baking.