Question

tori has a wardrobe that is 85 inches tall, 35 inches wide, and 25 inches long. she wants to buy a new wardrobe that is 90 inches tall, 32 inches wide, and 23 inches long. what is the difference in volume of the two wardrobes? \boxed{} in³

Explanation:

Step1: Calculate volume of old wardrobe

The volume \( V \) of a rectangular prism (wardrobe) is given by \( V = \text{length} \times \text{width} \times \text{height} \). For the old wardrobe, length = 25 in, width = 35 in, height = 85 in. So, \( V_{\text{old}} = 25\times35\times85 \).
Calculating: \( 25\times35 = 875 \), then \( 875\times85 = 74375 \) \( \text{in}^3 \).

Step2: Calculate volume of new wardrobe

For the new wardrobe, length = 23 in, width = 32 in, height = 90 in. Using the same volume formula, \( V_{\text{new}} = 23\times32\times90 \).
Calculating: \( 23\times32 = 736 \), then \( 736\times90 = 66240 \) \( \text{in}^3 \).

Step3: Find the difference in volumes

Subtract the volume of the new wardrobe from the old one: \( \text{Difference} = V_{\text{old}} - V_{\text{new}} = 74375 - 66240 \).
Calculating: \( 74375 - 66240 = 8135 \) \( \text{in}^3 \).

Answer:

8135