Answer:
The surface area that Sergio needs to frost on each cake is 3,238 square centimeters
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The surface area of the cylindrical cake is equal to the lateral area plus the area of the top of cylinder (remember that the bottom of the cake does not need frosting)
so
[tex]SA=\pi r^{2}+2\pi r h[/tex]
we have
[tex]r=40.2/2=20.1\ cm[/tex] ---> the radius is half the diameter
[tex]h=15.6\ cm[/tex]
[tex]\pi=3.14[/tex]
substitute the given values
[tex]SA=(3.14)(20.1)^{2}+2(3.14)(20.1)(15.6)[/tex]
[tex]SA=1,268.59+1,969.16\\SA=3,237.75\ cm^2[/tex]
Round up to the nearest whole number
[tex]SA=3,238\ cm^2[/tex]
therefore
The surface area that Sergio needs to frost on each cake is 3,238 square centimeters
