Calculate Cuboid Volume: Square Base (16 cm²) with 6 cm Height

Q: Do I need to find the side length of the square base?

No! Since you already have the base area (16 cm²), you can calculate volume directly. The formula $ V = \text{Base Area} \times \text{Height} $ works perfectly here.

Q: Why is the answer in cubic centimeters?

Volume always uses cubic units! When you multiply area (cm²) by height (cm), you get cm³. This makes sense because volume measures 3-dimensional space.

Q: Would this work for any cuboid shape?

Yes! The formula $ V = \text{Base Area} \times \text{Height} $ works for any prism or cuboid, regardless of the base shape - square, rectangle, triangle, etc.

Q: Can I always calculate volume when given base area and height?

Absolutely! These two measurements are all you need for any prism. The shape of the base doesn't matter - circle, triangle, pentagon - the formula stays the same.

Volume Calculation with Given Base Area

Given an cuboid so that the base is a square

Given that the area of the base is 16 cm²

Height of the cuboid 6 cm

Is it possible to calculate the volume of the cuboid?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the volume of the box if possible

00:03 Base is a square according to the data, so sides are equal

00:07 The square's perimeter equals the sum of its sides

00:10 The square's perimeter equals the sum of its sides

00:14 This is side A

00:20 Let's draw the box

00:36 Write down the sides we know

00:39 Height times length times width

00:42 Let's substitute appropriate values and solve for the volume

00:45 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

Given an cuboid so that the base is a square

Given that the area of the base is 16 cm²

Height of the cuboid 6 cm

Is it possible to calculate the volume of the cuboid?

Step-by-step solution

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

Step 1: Identify the given information.
Step 2: Apply the appropriate formula for the volume of the cuboid.
Step 3: Perform the necessary substitution.

Now, let's work through each step:
Step 1: The problem gives us the area of the base, which is 16 cm $^2$ , and the height of the cuboid, which is 6 cm.
Step 2: The formula to find the volume of a cuboid is given by:

$V = \text{Base Area} \times \text{Height}$

Step 3: Substitute the given values into the formula:

$V = 16 \, \text{cm}^2 \times 6 \, \text{cm}$

After substituting, we find that $V = 96 \, \text{cm}^3$ .

This means it is indeed possible to calculate the volume of the cuboid given the area of the base and the height.

Therefore, the answer is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Formula: Volume equals base area times height for any prism
Technique: Multiply directly: $16 \, \text{cm}^2 \times 6 \, \text{cm} = 96 \, \text{cm}^3$
Check: Units multiply correctly: cm² × cm = cm³ for volume ✓

Common Mistakes

Avoid these frequent errors

Trying to find individual side lengths first
Don't calculate the square's side length (4 cm) then multiply length × width × height = wrong approach! This wastes time and creates unnecessary steps. Always use the direct formula: Volume = Base Area × Height when base area is given.

Practice Quiz

Test your knowledge with interactive questions

Calculate the volume of the rectangular prism below using the data provided.

FAQ

Everything you need to know about this question

Do I need to find the side length of the square base?

No! Since you already have the base area (16 cm²), you can calculate volume directly. The formula $V = \text{Base Area} \times \text{Height}$ works perfectly here.

Why is the answer in cubic centimeters?

Volume always uses cubic units! When you multiply area (cm²) by height (cm), you get cm³. This makes sense because volume measures 3-dimensional space.

Would this work for any cuboid shape?

Yes! The formula $V = \text{Base Area} \times \text{Height}$ works for any prism or cuboid, regardless of the base shape - square, rectangle, triangle, etc.

What if I calculated the side length anyway?

You'd still get the right answer! If the base area is 16 cm², each side is 4 cm, so $V = 4 \times 4 \times 6 = 96 \, \text{cm}^3$ . But the direct method is faster and less error-prone.

Can I always calculate volume when given base area and height?

Absolutely! These two measurements are all you need for any prism. The shape of the base doesn't matter - circle, triangle, pentagon - the formula stays the same.

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