Calculate Cuboid Volume: 4 Equal Orthohedra with AB=4 and BC=3/4AB

Shown below is a large cuboid composed of 4 smaller orthohedra equal in size.

$AB=4$

$BC=\frac{3}{4}AB$

$BE=\frac{1}{2}AB$

Calculate the volume of the large cuboid.

Video Solution

Solution Steps

00:00 Calculate the volume of the large box

00:03 BC size according to the data, substitute AB value and solve for BC

00:10 This is BC size

00:13 BE size according to the data, substitute AB value and solve for BE

00:17 This is BE size

00:22 The volume of the large box equals 4 volumes of small box

00:28 Let's use the formula for calculating box volume

00:31 width times height times length

00:35 Let's substitute appropriate values and solve for volume

00:43 And this is the solution to the question

Step-by-Step Solution

To solve the problem, let's determine the dimensions of the large cuboid:

Step 1: Identify the given values: $AB = 4$ , $BC = \frac{3}{4} \times AB$ , and $BE = \frac{1}{2} \times AB$ .
Step 2: Calculate the dimensions of the cuboid:

$\text{Volume} = AB \times BC \times BE = 4 \times 3 \times 2 = 24$ .
Since the large cuboid is composed of four equal orthohedra, the volume of the entire large cuboid is $4 \times 24 = 96 \, \text{cm}^3$ .

So, the volume of the large cuboid is $96 \, \text{cm}^3$ .