Find the Square Base Side Length of a Cuboid with Volume 640 cm³ and Height 10

Question

Given the following cuboid such that its base is a square.

The height of the cuboid is equal to 10 The volume of the cuboid is equal to 640 cm³.

Find the length of the side of the base

00:00 Find the base edge of the box

00:04 The base of the box is a square according to the given data, therefore the edges are equal

00:11 We will use the formula for calculating box volume

00:14 Height multiplied by length multiplied by width

00:18 We will substitute appropriate values and solve to find A

00:22 Let's isolate A

00:28 When taking the square root, there are 2 solutions: negative and positive

00:31 The negative solution is not relevant, it must be a physical size

00:36 And this is the solution to the question

To find the length of the side of the square base, we'll apply the formula for the volume of a cuboid:

$V = l^2 \times h$

Step 1: Substitute the given values into the equation.

We have:

$640 = l^2 \times 10$

Step 2: Simplify the equation.

Divide both sides by 10:

$64 = l^2$

Step 3: Solve for $l$ .

Take the square root of both sides:

$l = \sqrt{64}$

$l = 8$

Thus, the length of the side of the base of the cuboid is $8$ cm.

$8$