Calculate Cuboid Volume: Rectangle Base 12 cm² with Height 3

Q: Why don't I need to find both length and width separately?

You already have the base area (12 cm²)! For volume, you only need area × height, not individual dimensions. The formula $ V = l \times w \times h $ becomes $ V = A_{base} \times h $ when area is given.

Q: How do I know which dimension is the height?

The height is always the dimension that extends vertically from the base. In this cuboid, the height is 3 cm - the distance from the bottom face ABCD to the top face EFGH.

Q: Can I solve this if the base wasn't a rectangle?

Absolutely! As long as you know the base area and height, you can find the volume of any prism using $ V = A_{base} \times h $, regardless of the base shape.

Q: What units should my answer have?

Since area is in cm² and height is in cm, volume will be in cm³ (cubic centimeters). Always cube the linear unit: $ cm² \times cm = cm³ $.

Volume Calculation with Given Base Area

ABCD is a rectagle that has an area of 12 cm².

Calculate the volume of the cuboid ABCDEFGH.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find the volume of the box, A B C D E F G H.

00:14 Remember, in a rectangle, opposite sides are equal.

00:18 We'll label the side, C D, with the letter X.

00:22 To find the area of a rectangle, multiply the length, C D, by the width, B D.

00:28 Now, let's plug in the values and solve for X.

00:32 Calculate the volume: length, six, times width, two, times height, three.

00:39 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

ABCD is a rectagle that has an area of 12 cm².

Calculate the volume of the cuboid ABCDEFGH.

Step-by-step solution

Based on the given data, we know that:

$BD=HF=2$

We also know the area of ABCD and the length of DB.

We can therefore substitute these values into the formula to find CD, which we will call $x$ :

$2\times x=12$

We can then divide both sides by 2:

$x=6$

Therefore, CD equals 6.

Finally, we can calculate the volume of the box as follows:

$6\times2\times3=12\times3=36$

Final Answer

$36$

Key Points to Remember

Essential concepts to master this topic

Formula: Volume of cuboid equals base area times height
Technique: Use $V = A_{base} \times h = 12 \times 3 = 36$
Check: Verify base area calculation: $2 \times 6 = 12$ cm² ✓

Common Mistakes

Avoid these frequent errors

Trying to find individual length and width when only area is given
Don't waste time finding exact dimensions when you already have the base area = confusion and wrong calculations! The diagram shows one dimension (2) to verify the area, not for the volume calculation. Always use Volume = Base Area × Height directly when area is given.

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 don't I need to find both length and width separately?

You already have the base area (12 cm²)! For volume, you only need area × height, not individual dimensions. The formula $V = l \times w \times h$ becomes $V = A_{base} \times h$ when area is given.

What does the number 2 in the diagram represent?

The 2 represents one dimension of the rectangle base. It's shown to help verify that the area is correct: if one side is 2 cm, the other must be 6 cm to get $2 \times 6 = 12$ cm².

How do I know which dimension is the height?

The height is always the dimension that extends vertically from the base. In this cuboid, the height is 3 cm - the distance from the bottom face ABCD to the top face EFGH.

Can I solve this if the base wasn't a rectangle?

Absolutely! As long as you know the base area and height, you can find the volume of any prism using $V = A_{base} \times h$ , regardless of the base shape.

What units should my answer have?

Since area is in cm² and height is in cm, volume will be in cm³ (cubic centimeters). Always cube the linear unit: $cm² \times cm = cm³$ .

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Calculate Cuboid Volume: Rectangle Base 12 cm² with Height 3

Volume Calculation with Given Base Area

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why don't I need to find both length and width separately?

What does the number 2 in the diagram represent?

How do I know which dimension is the height?

Can I solve this if the base wasn't a rectangle?

What units should my answer have?

🌟 Unlock Your Math Potential

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