Answer:
[tex]h \approx 1.125\,in[/tex]
Step-by-step explanation:
The volume of the original cake is:
[tex]V_{o} = \frac{\pi}{4}\cdot (6\,in)^{2}\cdot (2\,in)[/tex]
[tex]V_{o} \approx 56.549\,in^{3}[/tex]
The new height on the new cake pan is:
[tex]V_{o} = \frac{\pi}{4}\cdot (8\,in)^{2}\cdot h[/tex]
[tex]h \approx 1.125\,in[/tex]
Answer:
The cake will be 1.125 inches tall
Step-by-step explanation:
The initial diameter of the cake, d₁ = 6 inches
The initial height of the cake, h₁ = 2 inches
The initial radius of the cake, r₁ = d₁/2 = 6/2 = 3 inches
r₁ = 3 inches
Because the round cake has a height, it will take the form of a cylinder
The initial volume of the cake, V₁ = π r₁²h₁
V₁ = π * 3² * 2
V₁ = 18π inch³
When the batter is poured into a round cake pan
the diameter, d₂ = 8 inches
r₂ = 8/2 4 inches
Since the cake is still produced using the same recipe, the volume of the cake does not change, i.e. V₂ = V₁ = 18π inch³
To get the height of the new cake
V₂ = π r₂²h₂
18π = π * 4² * h₂
h₂ = 18/16
h₂ = 1.125 inches
The new height of the cake will be 1.125 inches
