When baking a cake you have a choice of the following pans: a round cake that is 2 inches deep and has a 7-inch diameter, a 6 in
ches times 9-inch rectangular cake pan that is 2 inches deep. Question: Excluding the bottom of the cake what is the surface area of each cake that will be covered by frosting?
I do not need an answer I just need help on this question. Thank you.
The answer is round cake - 82.42 in² rectangular cake - 114 in²
Round cake: d = 7 in r = d/2 = 7 in / 2 = 3.5 in h = 2 in
The surface are of a cylinder is: A = 2πr² + 2πrh
The surface are of the round cake (which is actually a cylindrical cake) excluding the bottom is: A = 2πr² + 2πrh - πr² A = πr² + 2πrh A = 3.14 * 3.5² + 2 * 3.14 * 3.5 * 2 = 38.46 + 43.96 = 82.42 in²
Rectangular cake: w = 6 in l = 9 in h = 2 in
The surface are of a rectangle is: 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 in²
