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 volume formula for 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 volume of first set

For the first set: \( l = 24 \) in, \( w = 16 \) in, \( h = 34 \) in.
\( V_1 = 24 \times 16 \times 34 \)
First, \( 24 \times 16 = 384 \), then \( 384 \times 34 = 13056 \) \( \text{in}^3 \).

Step3: Calculate volume of second set

For the second set: \( l = 22 \) in, \( w = 16 \) in, \( h = 36 \) in.
\( V_2 = 22 \times 16 \times 36 \)
First, \( 22 \times 16 = 352 \), then \( 352 \times 36 = 12672 \) \( \text{in}^3 \).

Step4: Find the difference in volumes

\( \text{Difference} = |V_1 - V_2| = |13056 - 12672| = 384 \) \( \text{in}^3 \).

Answer:

384