Cuboid Edge Length Problem: Finding Relationships When Edge = Base + 5

Q: Why isn't the volume just X³ + 5?

Because the cuboid isn't a cube! The base is X × X, but the height is X + 5. You can't just add 5 to a cube's volume formula. Always use base area × height.

Q: How do I remember which dimension is X + 5?

Look at the diagram carefully! The vertical edge (height) is labeled X + 5, while the base edges are both X. The height is what makes this a rectangular prism instead of a cube.

Q: Should I expand X²(X + 5) to get the final answer?

Not necessarily! $ X^2(X + 5) $ is the correct factored form. You could expand it to $ X^3 + 5X^2 $, but the factored form clearly shows base area times height.

Q: What if I confused which measurement was X + 5?

Always check the diagram! The problem states the edge is 5 greater than the base side. In a rectangular prism, this means the height is X + 5, not the base dimensions.

Q: Can I use V = length × width × height directly?

Absolutely! That gives V = X × X × (X + 5) = $ X^2(X + 5) $. This is the same as base area × height since the base area is X × X = X².

Volume Formulas with Rectangular Prisms

In an cuboid with a square base, the cuboid edge
It is greater by 5 of the base side.
We mark the side of the base with X,

What is true?

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Understand the problem

In an cuboid with a square base, the cuboid edge
It is greater by 5 of the base side.
We mark the side of the base with X,

What is true?

Step-by-step solution

To determine the volume of the cuboid, we need to follow these steps:

Step 1: Determine the area of the square base. Since the base is square with each side measuring $X$ , the area of the base is $X^2$ .
Step 2: Identify the height of the cuboid. The height is given as $X + 5$ .
Step 3: Use the volume formula for a cube, $V = \text{base area} \times \text{height}$ .

Let's execute these steps:
Step 1: The square base area is $X^2$ .
Step 2: The height of the cuboid, as given, is $X + 5$ .
Step 3: Plugging these into the volume formula gives $V = X^2 \times (X + 5) = X^2(X + 5)$ .

Thus, the expression for the volume of the cuboid is $V = X^2(X + 5)$ .

This matches the provided choice, confirming that the correct answer is $\boxed{V = X^2(X+5)}$ .

Final Answer

$V=X^2(X+5)$

Key Points to Remember

Essential concepts to master this topic

Base Area: Square base with side X has area X²
Height Formula: Edge length equals base side plus 5, so height = X + 5
Volume Check: Multiply base area by height: X² × (X + 5) = X²(X + 5) ✓

Common Mistakes

Avoid these frequent errors

Adding 5 to the volume instead of the height
Don't write V = X³ + 5 by adding 5 directly to a cubic volume! This ignores that only the height is 5 units longer than the base side. Always identify what measurement increases by 5, then use V = base area × height.

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 isn't the volume just X³ + 5?

Because the cuboid isn't a cube! The base is X × X, but the height is X + 5. You can't just add 5 to a cube's volume formula. Always use base area × height.

How do I remember which dimension is X + 5?

Look at the diagram carefully! The vertical edge (height) is labeled X + 5, while the base edges are both X. The height is what makes this a rectangular prism instead of a cube.

Should I expand X²(X + 5) to get the final answer?

Not necessarily! $X^2(X + 5)$ is the correct factored form. You could expand it to $X^3 + 5X^2$ , but the factored form clearly shows base area times height.

What if I confused which measurement was X + 5?

Always check the diagram! The problem states the edge is 5 greater than the base side. In a rectangular prism, this means the height is X + 5, not the base dimensions.

Can I use V = length × width × height directly?

Absolutely! That gives V = X × X × (X + 5) = $X^2(X + 5)$ . This is the same as base area × height since the base area is X × X = X².

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