A layered birthday cake has three rectangular prism layers. The base layer measures 16 inches by 12 inches. Each layer is two inches smaller in width and depth as the previous layer. All of the layers are 4 inches tall. What is the volume of the cake? *

The answer to your question is 732 in³

Step-by-step explanation:

Data

Rectangular prism layers

Base layer = 12 in x 10 in x 4 in

Second layer = 3 in smaller x 4 in

Volume = ?

Formula

Total volume = Volume of the base layer + Volume of the second layer

Total volume = length 1 x width 1 x height +  length 2 x width 2 x height

Substitution

Total volume = 12 x 10 x 4 + (12 - 3)(10 - 3)(4)

Simplification

Total volume = 480 + (9)(7)(4)

Total volume = 480 + 252

Result

Total volume = 732 in³