Calculate Cube Height from 16 cm² Base Area: Geometric Problem Solving

Q: How can I find height from just the base area?

A cube has all edges equal! Once you know the base area is $ 16 \text{ cm}^2 $, you can find the side length, which equals the height.

Q: Why is the height the same as the side length?

By definition, a cube is a regular 3D shape where length = width = height. This is what makes it different from a rectangular prism!

Q: What if this was a rectangular prism instead?

Then you'd be correct - you cannot find the height! Rectangular prisms can have different length, width, and height values, so base area alone wouldn't be enough.

Q: How do I remember the difference between cubes and other shapes?

Think of dice! A cube looks like a perfect dice - all faces are identical squares. If any face looks different, it's not a cube.

Q: Can I double-check my answer of 4 cm?

Yes! Calculate the base area using your answer: $ 4 \times 4 = 16 \text{ cm}^2 $. This matches the given information, so 4 cm is correct!

Cube Dimensions with Base Area

The cube shown below has a base area of 16 cm².

Is it possible to calculate the height of the cube? If so, what is it?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the height of the cube

00:04 Find the edges that will help us calculate the base area

00:08 Use the formula to calculate base area (height times length)

00:13 In a cube, all edges are equal

00:17 Substitute H for L (they are equal)

00:22 Extract the root and find the 2 possible solutions

00:31 H must be positive, as it is the length of an edge

00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The cube shown below has a base area of 16 cm².

Is it possible to calculate the height of the cube? If so, what is it?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the base area of the cube.
Step 2: Use the formula to find the side length of the base.
Step 3: Recognize that the height of the cube is equal to the side length of the base.

Now, let's work through each step:
Step 1: We are given the base area of the cube as $16 \, \text{cm}^2$ .
Step 2: The area of a square is calculated using the formula $\text{side}^2$ , where "side" is the length of each side of the square.
Setting up the equation: $\text{side}^2 = 16$ . Solving for the "side," we find $\text{side} = \sqrt{16} = 4 \, \text{cm}$ .
Step 3: Since the cube is a regular geometric shape, the height is equal to the side length of the base. Therefore, the height of the cube is $4 \, \text{cm}$ .

Therefore, the height of the cube is $4 \, \text{cm}$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Property: All edges of a cube have identical lengths
Technique: Find side length from area: $\text{side} = \sqrt{16} = 4 \text{ cm}$
Check: Verify height equals side: $4^2 = 16 \text{ cm}^2$ ✓

Common Mistakes

Avoid these frequent errors

Confusing cube with rectangular prism
Don't assume you need more information to find height = wrong reasoning! A cube has equal edges by definition, so base area gives all dimensions. Always remember that cube height equals side length of the base.

Practice Quiz

Test your knowledge with interactive questions

A cube has a total of 14 edges.

FAQ

Everything you need to know about this question

How can I find height from just the base area?

A cube has all edges equal! Once you know the base area is $16 \text{ cm}^2$ , you can find the side length, which equals the height.

Why is the height the same as the side length?

By definition, a cube is a regular 3D shape where length = width = height. This is what makes it different from a rectangular prism!

What if this was a rectangular prism instead?

Then you'd be correct - you cannot find the height! Rectangular prisms can have different length, width, and height values, so base area alone wouldn't be enough.

How do I remember the difference between cubes and other shapes?

Think of dice! A cube looks like a perfect dice - all faces are identical squares. If any face looks different, it's not a cube.

Can I double-check my answer of 4 cm?

Yes! Calculate the base area using your answer: $4 \times 4 = 16 \text{ cm}^2$ . This matches the given information, so 4 cm is correct!

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