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 × 9 inch rectangular cake pan that is 2 inches deep
a. Which of these pans has the larger volume? 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.
I just need help with b
Leave people alone get a live ok
These students can do whatever the hell they want let them be!
volumes are
round: πr^2h = π*(7/2)^2*2 = 98π/4 = 76.969 in^3
parallelopiped: LWH = 6*9*2 = 108 in^3
should be easy to tell now, eh?
areas are
round: πr^2 + 2πrh = πr(r+2h)
brick: LW+2LH+2WH = LW+2H(L+W)
Now plug in your numbers and compare
So...
Area for round pan: 3.14*3.5*2+2*3.14*3.5*3.5=98.91
and...
Area for rectangular pan:
9*6+2*9*2+2*6*2=114
Rose is right right?
I checked her work i got the same answers
Dude mis Valarie GET A LIFE this is the 4th cite you've messed up for these kids u probably upset Cuzco you manzanita left u for your sister get a cat
To find the surface area of each cake that will be covered by frosting, we need to calculate the area of the sides of the cakes.
a. Round cake pan:
First, find the circumference of the round cake pan by using the formula C = πd, where C represents circumference and d represents the diameter.
C = π × 7
C ≈ 22.0 inches
Now, find the height of the cake pan, which is given as 2 inches.
Next, multiply the circumference by the height to calculate the area of the sides of the round cake pan:
Area = C × height
Area = 22.0 × 2
Area = 44.0 square inches
b. Rectangular cake pan:
The dimensions of the rectangular cake pan are given as 6 inches by 9 inches, and the height is 2 inches.
To calculate the surface area of the sides of the rectangular cake pan, we need to find the perimeter of the rectangle and multiply it by the height.
Perimeter = 2 × (length + width)
Perimeter = 2 × (6 + 9)
Perimeter = 2 × 15
Perimeter = 30 inches
Now, multiply the perimeter by the height to calculate the area of the sides of the rectangular cake pan:
Area = Perimeter × height
Area = 30 × 2
Area = 60 square inches
Therefore, the surface area of the sides of the round cake pan that will be covered by frosting is 44.0 square inches, while the surface area of the sides of the rectangular cake pan that will be covered by frosting is 60 square inches.
Justification:
To calculate the surface area covered by frosting, we only consider the sides of the cake since the bottom is not frosted. We find the area of the sides of each cake pan. The round cake pan has a smaller surface area since it has a smaller circumference compared to the perimeter of the rectangular cake pan.