Calculate X: Finding Width in a 3×5×X Rectangular Prism with Volume 90 cm³

Q: Why do we multiply the dimensions and not add them?

Volume measures space inside a 3D shape. Think of it as layers: if you have 3 rows of 6 columns, each 5 units tall, you get 3 × 6 × 5 = 90 unit cubes filling the space!

Q: What if I get the formula mixed up?

Remember: V = l × w × h always! The order doesn't matter since multiplication is commutative, but all three dimensions must be multiplied together.

Q: How do I solve for the missing dimension?

Use inverse operations! If V = l × w × h, then to find one missing dimension, divide the volume by the product of the other two dimensions.

Q: What units should my answer have?

The missing dimension has the same units as the other dimensions. Since length and height are in cm, width X must also be in cm.

Q: Can I check my answer a different way?

Yes! Calculate the volume using your answer: $ 3 \times 6 \times 5 = 90 $. If you get the original volume, you're correct!

Volume Formulas with Missing Dimensions

A rectangular prism has a length of 3 cm and a height of 5 cm.

Its volume is equal to 90 cm3.

Calculate X.

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Understand the problem

A rectangular prism has a length of 3 cm and a height of 5 cm.

Its volume is equal to 90 cm3.

Calculate X.

Step-by-step solution

To find the missing width ( $X$ ) of the rectangular prism, we start with the volume formula for a rectangular prism:

$V = l \times w \times h$

Here, $l = 3 \, \text{cm}$ , $h = 5 \, \text{cm}$ , and $V = 90 \, \text{cm}^3$ . We need to find $w$ (or $X$ ).

Substitute the known values into the formula:

$90 = 3 \times X \times 5$

Simplifying, we have:

$90 = 15 \times X$

To solve for $X$ , divide both sides of the equation by 15:

$X = \frac{90}{15}$

Calculating this gives:

$X = 6$

Therefore, the calculated width of the rectangular prism is $X = 6 \, \text{cm}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Volume Formula: For rectangular prisms, V = length × width × height
Technique: Substitute known values: 90 = 3 × X × 5 = 15X
Check: Verify by calculating: 3 × 6 × 5 = 90 cm³ ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't calculate 3 + X + 5 = 90 which gives X = 82! Volume requires multiplication of all three dimensions, not addition. Always use V = l × w × h and multiply the dimensions together.

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 the dimensions and not add them?

Volume measures space inside a 3D shape. Think of it as layers: if you have 3 rows of 6 columns, each 5 units tall, you get 3 × 6 × 5 = 90 unit cubes filling the space!

What if I get the formula mixed up?

Remember: V = l × w × h always! The order doesn't matter since multiplication is commutative, but all three dimensions must be multiplied together.

How do I solve for the missing dimension?

Use inverse operations! If V = l × w × h, then to find one missing dimension, divide the volume by the product of the other two dimensions.

What units should my answer have?

The missing dimension has the same units as the other dimensions. Since length and height are in cm, width X must also be in cm.

Can I check my answer a different way?

Yes! Calculate the volume using your answer: $3 \times 6 \times 5 = 90$ . If you get the original volume, you're correct!

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