Question

Kristen owns a bakery and is making a cake for a wedding. The dimensions of the cake are shown below. Answer each of the questions below.

1. What is the frosted area of the top cake? (Round to the nearest tenth)

2. What is the frosted area of the bottom cake? (Round to the nearest tenth)

3. What is the total surface area of cake that will be frosted?

Answer 1

Given:

A picture of a cake is given attached with this question. All the dimensions are given.

To find:

1. We have to find the frosted area of the top cake.

2. Find frosted area of bottom cake.

3. Find to total surface area to be frosted.

Step-by-step explanation:

1. Top cake frosted area:

Diameter of the top cake $= 38 - 13 - 13 = 12 \textrm { mm}$

Top area of the top cake $= \pi (\frac{12}{2}) ^{2} = 113.09 \textrm { sq. mm}$

Side surface area of the top cake $= (23 - 14) \times 2\pi (\frac{12}{2} ) = 339.29 \textrm { sq. mm}$

So, total frosted area of the top cake $= (113.09 + 339.29) = 452.4 \textrm { sq. mm}$

2. Bottom cake frosted area:

Top area of the bottom cake $= \pi (\frac{38}{2} )^{2} = 1134.11 \textrm { sq. mm}$

Side surface area of the bottom cake $= 14 \times 2\pi (\frac{38}{2} ) = 1671.33 \textrm { sq. mm}$

So, total frosted area of the bottom cake $= 1134.11 + 1671.33 - 113.09 = 2692.3 \textrm { sq. mm}$

3. The total surface area to be frosted $= 452.4 + 2692.3 = 3144.7 \textrm { sq. mm}$