Calculate the Volume: Cuboid with Dimensions 4×2×5 Containing Equal Parts

Shown below is a cuboid containing 5 smaller cuboids of equal size.

AB = 4

BE = 2

EK = 5

Calculate the volume of the large cuboid.

Video Solution

Solution Steps

00:00 Calculate the volume of the large box

00:03 We'll use the formula for calculating box volume

00:07 width times height times length

00:12 We'll substitute appropriate values and solve for the volume

00:23 This is the volume of the small box

00:26 The volume of the large box equals 5 times the volume of the small box

00:37 We'll substitute the value of the small box volume and solve for the volume

00:40 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the volume of one smaller cuboid.
Step 2: Multiply the volume of one smaller cuboid by the number of cuboids (5) to find the total volume of the large cuboid.

Now, let's work through each step:
Step 1: The dimensions for each smaller cuboid are given as:

Using the volume formula for a cuboid, we find the volume of one smaller cuboid:

V_{\text{small}} = 4 \times 2 \times 5 = 40 \, \text{cm}^3

Step 2: Since there are 5 such smaller cuboids, the total volume for the large cuboid is:

V_{\text{large}} = 5 \times 40 = 200 \, \text{cm}^3

Therefore, the volume of the large cuboid is $200 \, \text{cm}^3$ .