When baking a cake, you have a choice of the following pans: a round cake pan that is 2 inches deep and has a 7 inch diameter.
a 6 inch x9 inch rectangular cake pan that is 2 inches deep.
A. which of these pans has the larger value? Justify your answer.
B. Excluding the bottom of the cake, what is the surface area of each cake that will be covered by frosting? Justify your answer.
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Find the volume of each pan.
V = pi * r^2 * H
V = LWH
Once you've answered A, I'll help you with B.
or she/he probably was just covering their identity as a "tutor" because truth is literally on every forum for this question. so its probably a kid tryna get answers like us
A. To determine which pan has the larger value, we need to compare the volumes of the two pans. The volume of a cylinder (such as the round cake pan) can be calculated using the formula V = πr^2h, where r is the radius and h is the height. The volume of a rectangular prism (such as the rectangular cake pan) can be calculated using the formula V = lwh, where l, w, and h are the length, width, and height, respectively.
For the round cake pan:
Radius (r) = 7 inches / 2 = 3.5 inches
Height (h) = 2 inches
V = π(3.5^2)(2) ≈ 24.50π in^3
For the rectangular cake pan:
Length (l) = 9 inches
Width (w) = 6 inches
Height (h) = 2 inches
V = (9)(6)(2) = 108 in^3
Comparing the two volumes, we see that 108 in^3 is larger than 24.50π in^3. Therefore, the rectangular cake pan has the larger value.
B. To find the surface area that will be covered by frosting, we need to calculate the surface area of each cake excluding the bottom.
For the round cake pan, the surface area of the cylinder (excluding the bottom) can be calculated using the formula SA = 2πrh + πr^2, where r is the radius and h is the height.
SA = 2π(3.5)(2) + π(3.5^2) ≈ 44.00π in^2
For the rectangular cake pan, the surface area of the rectangular prism (excluding the bottom) can be calculated using the formula SA = 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height, respectively.
SA = 2(9)(6) + 2(9)(2) + 2(6)(2) = 132 in^2
Therefore, the round cake pan has a surface area of approximately 44.00π in^2 covered by frosting, while the rectangular cake pan has a total surface area of 132 in^2 covered by frosting.