Calculate Volume Difference: Nested Cuboids with Dimensions 4×5×3

Given the small cuboid ABKD

inside the large cuboid

Given the small cuboid fits 4 times the large cuboid

BC=4 AB=5 BK=3

What is the volume of the large cuboid minus the small cuboid?

Video Solution

Solution Steps

00:00 Find the volume difference between the boxes

00:03 We'll use the formula to calculate box volume

00:07 width times height times length

00:13 We'll substitute appropriate values and solve for the volume

00:29 This is the volume of the small box

00:34 The small box fits 4 times in the large box

00:38 We'll subtract the small box volume from the large box volume to find the difference

00:41 We'll use the volume value we found and solve for the difference

00:44 And this is the solution to the problem

Step-by-Step Solution

To solve the problem, we'll start by calculating the volume of the small cuboid.

Step 1: Volume of the small cuboid
The small cuboid dimensions are $AB = 5$ , $BC = 4$ , and $BK = 3$ . Hence, its volume is:

$V = 5 \times 4 \times 3 = 60 \, \text{cm}^3$

Step 2: Volume of the large cuboid
Since the small cuboid fits four times into the large cuboid, the volume of the large cuboid is:

$4 \times 60 = 240 \, \text{cm}^3$

Step 3: Volume of the large cuboid minus the small cuboid
Subtracting the volume of the small cuboid from the large cuboid, we have:

$240 - 60 = 180 \, \text{cm}^3$

Thus, the volume of the large cuboid minus the small cuboid is $\boxed{180 \, \text{cm}^3}$ .