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

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 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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