Question

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 a. Which of these pans has the larger volume? Justify your answer. b. How much icing will be needed to frost each cake, excluding the bottom of the cake? Justify your answer.

Answer 1

Round pan volume is:
3.14•r^2•h
D=7 so r=3.5 in
3.14• (3.5^2)•2 = 76.97 in^3

Rec. pan vol. is :
9•6•2= 108 in^3

Rec. Pan is larger because 108 in^3 is > 76.97 in^3 :) .

The icing that will be needed to frost the round cake pan is:
We need to find the surface area:
S.A= 3.14r^2 + 2 • 3.14•r • h .... 3.14 is the value of PI
So, S.A= 3.14• 3.5^2 + 6.28• 3.5• 2= 82.47 in^2 the icing that'll be needed to frost the round cake pan.

Icing that will be needed for the rec. cake pan is:

2•9•2=36 in^2
6•9•2= 108in^2
6•2= 12 in^2
S.A= 156 in^2 the icing needed to frost the rec. cake pan .... the S.A of all sides except the bottom one :).

Good luck ;-)