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.
To find the volume of each pan, we need to use the formula for the volume of a cylinder (since a round pan is essentially a cylinder) and the formula for the volume of a rectangular prism (since a rectangular pan is essentially a rectangular prism).
The volume of the round cake pan can be calculated as follows:
Volume = π × (radius)2 × height
Radius = diameter ÷ 2 = 7 ÷ 2 = 3.5
Volume = π × 3.52 × 2
Volume ≈ 77.7 cubic inches
The volume of the rectangular cake pan can be calculated as follows:
Volume = length × width × height
Volume = 6 × 9 × 2
Volume = 108 cubic inches
Therefore, the rectangular cake pan has a larger volume than the round cake pan.