Calculate Cuboid Height: Volume 90 cm³ with 10 cm Square Base

Given the following cuboid such that its base is a square. The length of the side of the base is equal to 10

The volume of the cuboid is equal to 90 cm³.

Find the length of the height

Video Solution

Solution Steps

00:00 Find the height of the box

00:03 The base of the box is a square according to the given data, therefore the sides are equal

00:12 We'll use the formula for calculating box volume

00:21 height times length times width

00:26 We'll substitute appropriate values and solve for height A

00:31 We'll isolate H

00:36 And this is the solution to the question

Step-by-Step Solution

To solve the problem of finding the height of the cuboid, we will follow these steps:

Now, let's work through each step:

Step 1: Calculate the square base area.
The side length of the square base is $s = 10$ cm. Thus, the area of the base is given by:

$\text{Area} = s^2 = 10^2 = 100$ cm $^2$ .

Step 2: Use the volume formula.
The volume of the cuboid is given by the formula:

$V = \text{base area} \times h$ .

We know the volume $V = 90$ cm $^3$ , and the base area is $100$ cm $^2$ . Therefore, we have:

$90 = 100 \times h$ .

To find the height $h$ , solve the equation:

$h = \frac{90}{100} = 0.9$ cm.

Therefore, the solution to the problem is that the height of the cuboid is $0.9$ cm.