Question

Shynna designed her perfect wedding cake. She wants to have 3 layers with smooth white frosting on the cake. The first layer will have a 24-inch diameter, the second layer will have an 18-inch diameter and the top layer will have a 10-inch diameter. Each layer will be 6-inches tall. How many square inches of frosting will show on the surface of the cake?

Answer 1

Answer:

Step-by-step explanation:

979.68 in^2.

Step 1: Calculate the surface area of each layer using the formula for the lateral surface area of a cylinder:

�

=

2

�

�

ℎ

A=2πrh.

Step 2: For the first layer, the radius

�

1

r

1

​

 is half the diameter, which is

24

2

=

12

2

24

​

=12 inches. The height h is 6 inches. So, the surface area of the first layer is

�

1

=

2

�

×

12

×

6

A

1

​

=2π×12×6.

Step 3: For the second layer, the radius

�

2

r

2

​

 is half the diameter, which is

18

2

=

9

2

18

​

=9 inches. The height h is 6 inches. So, the surface area of the second layer is

�

2

=

2

�

×

9

×

6

A

2

​

=2π×9×6.

Step 4: For the top layer, the radius

�

3

r

3

​

 is half the diameter, which is

10

2

=

5

2

10

​

=5 inches. The height h is 6 inches. So, the surface area of the top layer is

�

3

=

2

�

×

5

×

6

A

3

​

=2π×5×6.

Step 5: Add the surface areas of all the layers to get the total surface area of frosting.

Step 6: Calculate the total surface area using the values from Step 2, Step 3, and Step 4:

�

=

�

1

+

�

2

+

�

3

=

2

�

×

12

×

6

+

2

�

×

9

×

6

+

2

�

×

5

×

6

A=A

1

​

+A

2

​

+A

3

​

=2π×12×6+2π×9×6+2π×5×6