We are asked to determine which of the given pans will hold more cake batter, the pan or two round pans. To do so, we need to find the of each pan. Let's start with the rectangular pan. Note that this pan is in the shape of a . Recall that the volume of a rectangular prism with length
ℓ, width
w, and height
h can be calculated using the following formula.
V=ℓwh
We are given that
ℓ=9, w=13, and
h=2, so we have enough information to calculate the volume of the rectangular prism.
The volume of the rectangular pan is
234 cubic inches. Next, we will find the volume of the round pan. Notice that this pan is in the shape of a . The with the
r and height
h can be calculated by the following formula.
V=πr2h
In this case, we are given the and the height of the cylinder. To find the radius we can divide the diameter
d by
2.
We got that the radius of the cylinder is
4 inches. Now, we can substitute the height and the radius into the formula and calculate the volume of the cylinder.
V=πr2h
V=π(4)2(2)
V=π(16)(2)
V=π(32)
V=100.530…
V≈101
The volume of the round pan is about
101 cubic inches. Therefore, the volume of two round pans is about
2⋅101 or about
202 cubic inches. Finally, we can compare the volume of the rectangular pan with the volume of two round pans.
234>202
We can see that the volume of the rectangular pan is greater than the volume of two round pans. Therefore, the rectangular pan will hold more cake batter than two round pans.