Question

patricia is deciding between two sets of kitchen cabinets, both of which are shaped as rectangular prisms. the first set is 34 inches tall, 24 inches deep, and 16 inches wide. the second set is 36 inches tall, 22 inches deep, and 16 inches wide. what is the difference in the volume of the two sets of cabinets? \boxed{} in³

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Step2: Calculate the volume of the first set of cabinets

For the first set, \( l = 24 \) inches, \( w = 16 \) inches, \( h = 34 \) inches.
\( V_1 = 24\times16\times34 \)
\( 24\times16 = 384 \)
\( 384\times34 = 13056 \) cubic inches.

Step3: Calculate the volume of the second set of cabinets

For the second set, \( l = 22 \) inches, \( w = 16 \) inches, \( h = 36 \) inches.
\( V_2 = 22\times16\times36 \)
\( 22\times16 = 352 \)
\( 352\times36 = 12672 \) cubic inches.

Step4: Find the difference in volumes

\( \text{Difference} = |V_1 - V_2| \)
\( |13056 - 12672| = 384 \)

Answer:

384