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

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

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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