Answer this question: When baking a cake, you have the choice of the following pans: Pan 1. A round cake that Is 2 inches deep and has a 7 inch diameter. Pan 2. A 6 inch x 9 inch rectangular cake pan that is 2 inches deep. Which of these pans Has the largest volume? Justify your answer.
To compare the volumes of the two pans, we need to calculate the volume of each.
For Pan 1, the volume can be calculated using the formula for the volume of a cylinder: V = πr²h, where r is the radius (half the diameter) and h is the height (depth) of the cake. So, for Pan 1:
r = 7/2 = 3.5 inches
h = 2 inches
V = π(3.5)²(2) ≈ 77.0 cubic inches
For Pan 2, the volume can be calculated using the formula for the volume of a rectangular prism: V = lwh, where l is the length, w is the width, and h is the height (depth) of the cake. So, for Pan 2:
l = 9 inches
w = 6 inches
h = 2 inches
V = (9)(6)(2) = 108 cubic inches
Therefore, Pan 2 (the rectangular pan) has the largest volume, with a volume of 108 cubic inches.