area, circumference of a circle, volume

Question

Aaron creates a stacked cake comprised of three cylindrical sections as picture below, 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

So the radius of each cylindrical section increases by 2 inches.

 

The top cylinder has area 12.56 square inches.

Area = pi * radius^2 

 

12.56 = pi * radius^2

 

 4 = radius^2 <--- divides both sides by pi

 

radius = 2  <--- takes square root of both sides; radius must be positive, so -2 is rejected

 

So the smallest cylinder at the top has radius 2, and it is yellow.

 

The middle section then has radius 4 with color not given.

 

The bottom section has radius 6.

The area of the visible portion of the bottom cylinder in green is

 pi * 6^2 = 113.04 square inches