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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 inches 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.

Verified Answer :

JcAlmighty

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

adioabiola

The surface area of cylindrical and rectangular cake that will be covered by frosting excluding the bottom of the cake is 82.42 in² and 114 in² respectively

How to calculate surface area

  • Diameter of the cake = 7 in

  • Radius = Diameter/2

= 7 in / 2

= 3.5 in

  • Height of the cake = 2 in

The surface area of the cake (cylinder shape) excluding the bottom:

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 pan:

width = 6 in

length = 9 in

height = 2 in

The surface are of the rectangular cake excluding the bottom:

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

A = wl + 2wh + 2lh

A = 6 × 9 + 2 × 6 × 2 + 2 × 9 × 2

= 54 + 24 + 36

= 114 in²

Learn more about surface area:

https://brainly.com/question/6613758

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