To find the volume of each pan, we need to use the formula for the volume of a cylinder (V = πr^2h) for the round pan and the formula for the volume of a rectangular prism (V = lwh) for the rectangular pan.
Round pan:
radius = 7/2 = 3.5 inches
height = 2 inches
V = π(3.5)^2(2) = 24.46π cubic inches
Rectangular pan:
length = 9 inches
width = 6 inches
height = 2 inches
V = (9)(6)(2) = 108 cubic inches
Therefore, the rectangular pan has a larger volume than the round pan (108 cubic inches vs. 24.46π cubic inches).
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
Which of these pans has the larger volume? Justify your answer.
1 answer
1 answer