Calculate Base Area of Orthohedron: Given Volume 80 cm³ and 4m Edge

Volume Formulas with Unit Conversion

Look at the following orthohedron:

444

The volume of the orthohedron is 80 cm3 80~cm^3 .

The length of the lateral edge is 4 meters.

What is the area of the base of the orthohedron?
(shaded orange in the diagram)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the base area
00:03 The base area equals the box length multiplied by its width
00:24 The base area is a rectangle therefore all angles are right angles
00:28 We'll use the formula for calculating box volume
00:32 Width multiplied by height multiplied by length
00:35 Insert the appropriate values into the formula according to the given data and solve in order to find the area
00:46 Our aim is to determine the product of the height and width together
01:03 Let's isolate the area
01:06 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following orthohedron:

444

The volume of the orthohedron is 80 cm3 80~cm^3 .

The length of the lateral edge is 4 meters.

What is the area of the base of the orthohedron?
(shaded orange in the diagram)

2

Step-by-step solution

The formula for the volume of a box is height*length*width

In the specific question, we are given the volume and the height,

and we are looking for the area of the base,

As you will remember, the area is length * width

If we replace all the data in the formula, we see that:

4 * the area of the base = 80

Therefore, if we divide by 4 we see that

Area of the base = 20

3

Final Answer

20 cm²

Key Points to Remember

Essential concepts to master this topic
  • Volume Formula: For rectangular solids, Volume = Base Area × Height
  • Technique: Rearrange to Base Area = Volume ÷ Height = 80 ÷ 4
  • Check: Verify units match: convert 4m to 400cm, then 80 ÷ 400 = 0.2 cm² ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to convert units before calculating
    Don't use 4 meters directly with 80 cm³ = wrong answer of 20 cm²! The units don't match, so your calculation is meaningless. Always convert to matching units first: 4m = 400cm, then 80 ÷ 400 = 0.2 cm².

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.

121212888555

FAQ

Everything you need to know about this question

Why do I need to convert meters to centimeters?

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Because the volume is given in cm³ and the height is in meters! You must use the same units throughout your calculation, or your answer will be wrong.

How do I remember the volume formula for a rectangular solid?

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Think of it as Base Area × Height. The base area tells you the 'footprint' of the shape, and multiplying by height gives you the full 3D volume!

What if I get a very small answer like 0.2 cm²?

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That's correct! When you have a large height (400cm) and moderate volume (80 cm³), the base area must be small to make the multiplication work out.

Can I work backwards from volume to find other measurements?

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Absolutely! The volume formula V=l×w×h V = l \times w \times h can be rearranged:

  • Base Area = Volume ÷ Height
  • Height = Volume ÷ Base Area

How do I check if my unit conversion is right?

+

Remember: 1 meter = 100 centimeters. So 4m = 4 × 100 = 400cm. Always multiply by 100 when converting meters to centimeters!

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