Calculate Cuboid Volume: Using Rectangle Area of 20 cm²

Q: How do I know which face is rectangle DBFH?

Look at the diagram carefully! Rectangle DBFH is a vertical face of the cuboid. The vertices D, B, F, H form one of the rectangular faces, not the base.

Q: Why do I divide 20 by 4 to find the missing dimension?

Because Area = length × width. If we know the area is 20 cm² and one dimension is 4 cm, then the other dimension must be 20 ÷ 4 = 5 cm.

Q: What's the difference between area and volume?

Area measures flat surfaces (2D) in square units like cm². Volume measures space inside 3D shapes in cubic units like cm³. Volume needs all three dimensions!

Q: Can I use a different face's area to solve this?

You must use the given face DBFH with area 20 cm². Using a different face would give you different dimensions and lead to an incorrect volume calculation.

Volume Calculations with Given Face Areas

If the area of the rectangle DBFH is 20 cm².

Determine the volume of the cuboid ABCDEFGH.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the volume of the box ABCDEFGH

00:05 Data values

00:10 Let's mark the side BF with the letter X

00:13 The formula for calculating rectangle area - length (BF) multiplied by width (HF)

00:16 Let's substitute appropriate values and solve for X

00:21 Calculate volume by length(8) multiplied by width(4) multiplied by height(5)

00:24 And this is the solution to the question

Step-by-step written solution

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Understand the problem

If the area of the rectangle DBFH is 20 cm².

Determine the volume of the cuboid ABCDEFGH.

Step-by-step solution

We know the area of DBHF and the length of HF.

We will substitute the given data into the formula in order to find BF. Let's mark the side BF as X:

$4\times x=20$

We'll divide both sides by 4:

$x=5$

Therefore, BF equals 5

Now we can calculate the volume of the box:

$8\times4\times5=32\times5=160$

Final Answer

$160$ cm³

Key Points to Remember

Essential concepts to master this topic

Rectangle Area Formula: Area equals length times width for rectangles
Finding Unknown Dimensions: From area 20 and width 4, calculate $20 ÷ 4 = 5$
Volume Verification: Check by multiplying all three dimensions: $8 × 4 × 5 = 160$ ✓

Common Mistakes

Avoid these frequent errors

Using the wrong face for area calculation
Don't assume any rectangle has area 20 without identifying which face DBFH represents! This leads to using wrong dimensions in volume formula. Always identify which specific face corresponds to the given area before finding unknown dimensions.

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

How do I know which face is rectangle DBFH?

Look at the diagram carefully! Rectangle DBFH is a vertical face of the cuboid. The vertices D, B, F, H form one of the rectangular faces, not the base.

Why do I divide 20 by 4 to find the missing dimension?

Because Area = length × width. If we know the area is 20 cm² and one dimension is 4 cm, then the other dimension must be 20 ÷ 4 = 5 cm.

What's the difference between area and volume?

Area measures flat surfaces (2D) in square units like cm². Volume measures space inside 3D shapes in cubic units like cm³. Volume needs all three dimensions!

Can I use a different face's area to solve this?

You must use the given face DBFH with area 20 cm². Using a different face would give you different dimensions and lead to an incorrect volume calculation.

How do I check if my volume answer is correct?

Verify by checking that your three dimensions make sense:

Does $4 × 5 = 20$ cm² for face DBFH? ✓
Does $8 × 4 × 5 = 160$ cm³ for volume? ✓

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Calculate Cuboid Volume: Using Rectangle Area of 20 cm²

Volume Calculations with Given Face Areas

❤️ 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

How do I know which face is rectangle DBFH?

Why do I divide 20 by 4 to find the missing dimension?

What's the difference between area and volume?

Can I use a different face's area to solve this?

How do I check if my volume answer is correct?

🌟 Unlock Your Math Potential

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