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

Q: Why do we use l² instead of l × w in the formula?

Because the base is a square! In a square, all sides are equal, so length = width = l. Therefore, $ l \times l = l^2 $.

Q: How do I know which measurement is the height?

The problem clearly states "The height of the cuboid is equal to 10". Height is typically the vertical measurement, while the base measurements are horizontal.

Q: Can I solve this problem in a different order?

Yes! You could also write $ l^2 = \frac{640}{10} $ first, then calculate $ l^2 = 64 $, and finally $ l = 8 $. The steps are the same!

Q: What units should my final answer have?

Since the volume is given in cm³ and height in implied cm, your side length should be in cm. Always match the units given in the problem.

Volume Calculations with Square-Based Cuboids

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

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.

Final Answer

$8$

Key Points to Remember

Essential concepts to master this topic

Formula: For square-based cuboids, V = l² × h where l is side length
Technique: Divide volume by height first: 640 ÷ 10 = 64 = l²
Check: Verify by calculating: 8² × 10 = 64 × 10 = 640 cm³ ✓

Common Mistakes

Avoid these frequent errors

Using wrong volume formula for square base
Don't use V = length × width × height with different values for length and width = overcomplicated calculation! A square base means both sides are equal, so use V = l² × h. Always remember that square-based means the base has equal sides.

Practice Quiz

Test your knowledge with interactive questions

Calculate the volume of the rectangular prism below using the data provided.

FAQ

Everything you need to know about this question

Why do we use l² instead of l × w in the formula?

Because the base is a square! In a square, all sides are equal, so length = width = l. Therefore, $l \times l = l^2$ .

What if I get a decimal when taking the square root?

That's normal for many problems! Use a calculator for non-perfect squares. In this case, $\sqrt{64} = 8$ works out perfectly because 64 is a perfect square.

How do I know which measurement is the height?

The problem clearly states "The height of the cuboid is equal to 10". Height is typically the vertical measurement, while the base measurements are horizontal.

Can I solve this problem in a different order?

Yes! You could also write $l^2 = \frac{640}{10}$ first, then calculate $l^2 = 64$ , and finally $l = 8$ . The steps are the same!

What units should my final answer have?

Since the volume is given in cm³ and height in implied cm, your side length should be in cm. Always match the units given in the problem.

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