Word problem with 3 stacked cylinders

Question

Aaron creates a stacked cake comprised of three cylindrical sections and plans to cover the top of each section with a different color icing. Each lower section is a total of two inches wider than the section above it. If the yellow top of the upper section has an area of 12.56 square inches, what is the approximate area of the green visible portion of the bottom section which he will need to cover with icing?

Answer 1

This problem may talk about cylinders, but this problem is about surface areas of the flat circular surfaces.  Let's start by working with the surface area of the given top circle.  The formula for the respective surface is just the area of the circle, A = πr².  We know the area (A) and π, so we can solve for r.  r = sqrt (A / π) = sqrt (12.56 / π) = 2 inches.  If the radius is 2 inches, then the diameter (or width) of the top section is 4 inches.

 

Now that we know the width of the top section, we can simply calculate the width of the middle and lower sections.  If each lower section is 2 inches wider than the section above it, that means that the middle section is 6 inches diameter (or width) and the lowest section is 8 inches diameter (or width).

 

Now that we know the diameter of the other sections, we can calculate the surface area of the other sections using the area of circle formula.  (Don't forget to convert your respective diameters to radii before plugging them into the area of circle formula.)  The middle section has a flat surface area of 28.27 square inches.  The lowest section has a flat surface area of 50.27 square inches.  Subtracting the one from the other gives us the exposed area of the bottom flat surface, 50.27 - 28.27 = 22 square inches.  Therefore one will need to cover the bottom flat surface with 22 square inches of green frosting.