Express Cube Volume in Terms of Side Length 'a': 3D Geometry Problem

Cube Volume with Side Length Variables

Express the volume of the cube below in terms of a.

aaa

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Express the volume of the cube
00:03 We'll use the formula for calculating the cube volume (edge length cubed)
00:07 We'll substitute appropriate values and solve to find the volume
00:10 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Express the volume of the cube below in terms of a.

aaa

2

Step-by-step solution

In this problem, we are tasked with expressing the volume of a cube given its side length a a .

To find the volume of the cube, we use the standard volume formula for a cube, which is given by:

V=side length3 V = \text{side length}^3

Since the side length of this cube is a a , we substitute a a into the formula:

V=a3 V = a^3

Thus, the volume of the cube in terms of a a is a3 a^3 .

We compare this with the provided answer choices:

  • Choice 1: a3 a^3
  • Choice 2: 6a3 6a^3
  • Choice 3: 6a2 6a^2
  • Choice 4: a2 a^2

Our computed volume a3 a^3 matches Choice 1.

Therefore, the correct choice is: a3 a^3 .

3

Final Answer

a3 a^3

Key Points to Remember

Essential concepts to master this topic
  • Volume Formula: For any cube, volume equals side length cubed
  • Technique: Side length a means volume = a × a × a = a3 a^3
  • Check: Verify units: length³ gives volume units, not area units ✓

Common Mistakes

Avoid these frequent errors
  • Confusing volume with surface area formulas
    Don't use 6a2 6a^2 for volume = surface area formula! This gives the total area of all six faces, not the space inside. Always use a3 a^3 for cube volume.

Practice Quiz

Test your knowledge with interactive questions

Identify the correct 2D pattern of the given cuboid:

444444999

FAQ

Everything you need to know about this question

Why is the volume a3 a^3 and not 6a3 6a^3 ?

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Volume measures the space inside the cube, which is length × width × height = a × a × a = a3 a^3 . The coefficient 6 would be used for surface area since a cube has 6 faces.

What's the difference between a2 a^2 and a3 a^3 ?

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a2 a^2 represents area (2D measurement), while a3 a^3 represents volume (3D measurement). Since a cube is 3-dimensional, we need the cubic power.

How do I remember the cube volume formula?

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Think "cube means cubed"! A cube has 3 equal dimensions, so you multiply the side length by itself 3 times: a × a × a = a3 a^3 .

What if the side length was a number instead of 'a'?

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The same rule applies! If the side length was 5 units, the volume would be 53=125 5^3 = 125 cubic units. The variable 'a' just means we don't know the specific number.

Why isn't it 6a2 6a^2 since cubes have 6 faces?

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That's the surface area formula! Volume asks "how much space is inside?" not "what's the total area of all faces?" For volume, we only care about length × width × height.

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