Bailey’s Cakes and Pastries baked a three-tiered cake for a wedding. The bottom tier is a rectangular prism that is 18 centimeters long, 12 centimeters wide, and 8 centimeters tall. The middle tier is a rectangular prism that is 12 centimeters long, 8 centimeters wide, and 6 centimeters tall. The top tier is a cube with edges of 4 centimeters each. What is the volume of each tier and of the entire cake?

The volume of any rectangular prism shaped object whose dimensions are 

a by b by c is given by the formula [tex]V=a\cdot b\cdot c[/tex].

The bottom tier has the shape of a rectangular prism with dimensions 18 by 12 by 8 cm, thus the volume of the bottom tier is 

         [tex]V_{b}=a\cdot b\cdot c=18\cdot 12\cdot 8=1,728[/tex] (cubed cm).


The middle tier has the shape of a rectangular prism with dimensions 12 by 8 by 6 cm, thus the volume of the middle tier is 

         [tex]V_{m}=a\cdot b\cdot c=12\cdot 8\cdot 6=576[/tex] (cubed cm)


The top tier has the shape of a rectangular prism with dimensions 4 by 4 by 4 cm, thus the volume of the top tier is 

         [tex]V_{t}=a\cdot b\cdot c=4\cdot 4\cdot 4=64[/tex] (cubed cm)


The volume of the entire cake is the sum of the volumes of each tier, thus:

 [tex]V_{cake}=V_{b}+V_{m}+V_{t}=1,728+576+64=2,368[/tex] (cubed cm)


Answer: 

 [tex]\displaystyle{ v_{bottom \ tier } =1,728 \ cm^3}[/tex]

 [tex]\displaystyle{ v_{middle \ tier} =576 \ cm^3}[/tex]

 [tex]\displaystyle{ v_{top \ tier} =64 \ cm^3}[/tex]

 [tex]\displaystyle{ v_{cake} =2,368 \ cm^3}[/tex]