Calculate Height X of Rectangular Prism: Volume 45 cm³ with 2.5 cm × 4 cm Base

Q: Why do we multiply length × width × height for volume?

Volume measures how much space is inside a 3D shape. For a rectangular prism, you're finding how many unit cubes fit inside by multiplying the three dimensions together.

Q: What if I get a decimal answer like 4.5?

Decimal answers are completely normal! 4.5 cm means 4 and a half centimeters, which is a valid measurement. Always express your final answer with proper units.

Q: Can I solve this by dividing the volume by just one dimension?

No! You need to divide by the area of the base first. Since base area = length × width = 10 cm², then height = volume ÷ base area = 45 ÷ 10 = 4.5 cm.

Volume Formula with Missing Height Variable

A rectangular prism has a length of 2.5 cm and a width of 4 cm.

The volume of the rectangular prism is equal to 45 cm3.

Calculate X.

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Understand the problem

A rectangular prism has a length of 2.5 cm and a width of 4 cm.

The volume of the rectangular prism is equal to 45 cm3.

Calculate X.

Step-by-step solution

To solve this problem, we'll calculate the height $X$ of the rectangular prism using the given volume.

The volume of a rectangular prism is calculated using the formula:

V = \text{length} \times \text{width} \times \text{height}

We have the following values:

Volume ( $V$ ) = $45 \, \text{cm}^3$
Length = $2.5 \, \text{cm}$
Width = $4 \, \text{cm}$

Substitute these numbers into the volume formula and solve for $X$ :

45 = 2.5 \times 4 \times X

First, calculate the product of the length and width:

2.5 \times 4 = 10

Substitute this back into the equation:

45 = 10 \times X

To isolate $X$ , divide both sides by 10:

X = \frac{45}{10} = 4.5

Thus, the height $X$ of the rectangular prism is $4.5 \, \text{cm}$ .

Final Answer

4.5

Key Points to Remember

Essential concepts to master this topic

Formula: Volume = length × width × height for rectangular prisms
Technique: Substitute known values: 45 = 2.5 × 4 × X
Check: Verify answer: 2.5 × 4 × 4.5 = 45 cm³ ✓

Common Mistakes

Avoid these frequent errors

Confusing which dimension is which
Don't randomly assign the given measurements to length, width, and height without reading carefully = wrong setup! The problem clearly states 2.5 cm is length and 4 cm is width, leaving X as height. Always identify each dimension based on the problem statement and diagram.

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 multiply length × width × height for volume?

Volume measures how much space is inside a 3D shape. For a rectangular prism, you're finding how many unit cubes fit inside by multiplying the three dimensions together.

What if I get a decimal answer like 4.5?

Decimal answers are completely normal! 4.5 cm means 4 and a half centimeters, which is a valid measurement. Always express your final answer with proper units.

Can I solve this by dividing the volume by just one dimension?

No! You need to divide by the area of the base first. Since base area = length × width = 10 cm², then height = volume ÷ base area = 45 ÷ 10 = 4.5 cm.

How do I know which dimension is X in the diagram?

Look carefully at the diagram labels! The problem states X is the height (vertical dimension), while 2.5 and 4 are the base dimensions. The green color coding helps identify X as the height.

What units should my final answer have?

Since volume is in cm³ and the other dimensions are in cm, your height must be in cm. Always match the units given in the problem!

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