Calculate Cuboid Volume: 10cm Width with 40% and 150% Proportional Dimensions

Given the cuboid whose width is 10 cm

Length is smaller in 40% of width

The height of the cuboid is 50% greater than its length

Calculate the volume of the cube

Video Solution

Solution Steps

00:00 Calculate the volume of the box

00:03 Width of the box according to the data

00:08 Length of the box according to the data

00:19 Convert 40 percent to a number

00:29 This is the length of the box

00:37 Height of the box according to the data

00:45 Convert 50 percent to a number

01:00 This is the height of the box

01:12 Use the formula to calculate box volume

01:15 Width multiplied by height multiplied by length

01:18 And this is the solution to the question

Step-by-Step Solution

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

Step 1: Determine the length of the cuboid as a percentage of the width.
Step 2: Calculate the height of the cuboid as a percentage increase from the length.
Step 3: Use the dimensions to calculate the volume of the cuboid.

Now, let's work through each step:

Step 1: Calculate the length:

$L = W \times (1 - 0.40) = 10 \, \text{cm} \times 0.60 = 6 \, \text{cm}$

Step 2: Calculate the height:

$H = L \times 1.50 = 6 \, \text{cm} \times 1.50 = 9 \, \text{cm}$

Step 3: Calculate the volume:

$V = W \times L \times H = 10 \, \text{cm} \times 6 \, \text{cm} \times 9 \, \text{cm} = 540 \, \text{cm}^3$

Therefore, the volume of the cuboid is $\mathbf{540 \, \text{cm}^3}$ .