Question

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?

1,728 cubic centimeters



2,368 cubic centimeters



2,664 cubic centimeters



64 cubic centimeters



576 cubic centimeters



38 cubic centimeters



16 cubic centimeters



Pairs



the top tier




the middle tier




the bottom tier




the entire cake

Answer 1

the top tier is 64 cubic centimeters

the middle tier is 576 cubic centimeters

the bottom tier is 1728 cubic centimeters

the entire cake is 2368 cubic centimeters

Answer 2

The volume of any rectangular prism shaped object whose dimensions are

a by b by c is given by the formula
`V=a\cdot b\cdot c`.

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


`V_(b)=a\cdot b\cdot c=18\cdot 12\cdot 8=1,728` (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


`V_(m)=a\cdot b\cdot c=12\cdot 8\cdot 6=576` (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


`V_(t)=a\cdot b\cdot c=4\cdot 4\cdot 4=64` (cubed cm)


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


`V_(cake)=V_(b)+V_(m)+V_(t)=1,728+576+64=2,368` (cubed cm)


Answer:


`\displaystyle{ v_(bottom \ tier ) =1,728 \ cm^3}`


`\displaystyle{ v_(middle \ tier) =576 \ cm^3}`


`\displaystyle{ v_(top \ tier) =64 \ cm^3}`


`\displaystyle{ v_(cake) =2,368 \ cm^3}`