Question

19. 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 x 9 inch rectangular cake ban that is 2 inches deep
Which of these pans has the larger volume? Justify your answer.

Answer 1

114 in²

Explanation:

The answer isround cake

- 82.42 in²rectangular cake - 114 in²

Round cake:

d = 7 inr =

d/2 = 7 in / 2 = 3.5 inh = 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 - πr²A = πr² + 2πrh

A = 3.14 * 3.5² + 2 * 3.14 * 3.5 * 2 = 38.46 + 43.96 = 82.42 in²

Rectangular cake:w = 6 inl = 9 inh = 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 - wlA = wl + 2wh + 2lhA = 6 * 9 + 2 * 6 * 2 + 2 * 9 * 2 = 54 + 24 + 36 = 114 in²