Question

When baking a cake, you have a choice of the following pans:

1. a round cake pan that is 2 inches deep and has a 7-inch diameter
2. a 6 inch × 9-inch rectangular cake pan that is 2 inches deep

Which of these pans has the larger volume? Justify your answer.

Answer 1

Rectangular cake. I believe

Answer 2

round cake - 82.42 in^2

rectangular cake - 114 in^2

Round cake:

d = 7 in

r= d/2 = 7 in /2 = 3.5 in

h = 2

The surface area of a cylinder is: A = 2pie r^2 + 2pie rh The surface are of the round cake (cylindrical cake) excluding the bottom is

Area = 2pie r^2 + 2pie rh - pie r^2

Area = pie r^2 + 2pie rh

Area = 3.14 * 3.5² + 2 * 3.14 * 3.5 * 2

= 38.46 + 43.96

= 82.42 in^2

Rectangular cake:

w = 6 in |= 9 in h = 2 in

The surface area of a rectangle

A = 2wl + 2wh + 2lh

The surface are of the rectangular cake excluding the bottom is

A = 2wl + 2wh + 2lh - wl

A = wl + 2wh + 2lh

A = 6 * 9 + 2* 6 * 2 +2 *9 * 2

= 54 + 24 +36

= 114 in^2