Calculate Surface Area: Cuboid with 25 cm² Base and 3 cm Height

Q: Why do I need to find the side length first?

You're given the area of the square base (25 cm²), but to calculate surface area, you need the side length. Since $ s^2 = 25 $, we get $ s = 5 \, \text{cm} $.

Q: How many faces does a cuboid have?

A cuboid has 6 faces total: 2 identical bases (top and bottom) and 4 rectangular sides. Don't forget to count them all!

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

Volume measures the space inside (length × width × height), while surface area measures all the outside surfaces added together.

Q: Can I use a different formula?

Yes! You can also think of it as: $ 2(lw + lh + wh) $ where l = w = 5 cm and h = 3 cm. Both methods give the same answer.

Surface Area with Square Base Cuboid

Given the cuboid whose square base is of size 25 cm²,

The height of the cuboid is 3 cm,

What is the surface area 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 surface area of the box

00:03 It's a square according to the given data, so all sides are equal

00:07 We'll use the formula for calculating the area of a square (side squared)

00:10 We'll substitute appropriate values and solve for side A

00:13 This is side A

00:24 Now we'll use the formula for calculating the surface area of a box

00:33 We'll substitute appropriate values and solve for the surface area

01:21 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 the cuboid whose square base is of size 25 cm²,

The height of the cuboid is 3 cm,

What is the surface area of the cuboid?

Step-by-step solution

Let's find the surface area of the cuboid step by step:

First, we determine the side length of the square base. Since the area of the square base is given as $25 \, \text{cm}^2$ , we have:

s^2 = 25 \implies s = \sqrt{25} = 5 \, \text{cm}

Now, using the surface area formula for a cuboid with a square base:

\text{Surface Area} = 2s^2 + 4s \times h

Substitute the values $s = 5 \, \text{cm}$ and $h = 3 \, \text{cm}$ :

\text{Surface Area} = 2(5^2) + 4(5)(3) = 2(25) + 60 = 50 + 60 = 110 \, \text{cm}^2

Therefore, the surface area of the cuboid is 110 cm².

Final Answer

110 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Surface Area = 2 base areas + 4 lateral areas
Technique: Find side length first: $s = \sqrt{25} = 5 \, \text{cm}$
Check: Count all 6 faces: top, bottom, and 4 sides ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include the top and bottom faces
Don't calculate only the 4 side faces = getting 60 cm² instead of 110 cm²! This misses the two square bases completely. Always include ALL 6 faces: 2 square bases plus 4 rectangular sides.

Practice Quiz

Test your knowledge with interactive questions

A cuboid is shown below:

What is the surface area of the cuboid?

FAQ

Everything you need to know about this question

Why do I need to find the side length first?

You're given the area of the square base (25 cm²), but to calculate surface area, you need the side length. Since $s^2 = 25$ , we get $s = 5 \, \text{cm}$ .

How many faces does a cuboid have?

A cuboid has 6 faces total: 2 identical bases (top and bottom) and 4 rectangular sides. Don't forget to count them all!

What's the difference between volume and surface area?

Volume measures the space inside (length × width × height), while surface area measures all the outside surfaces added together.

Can I use a different formula?

Yes! You can also think of it as: $2(lw + lh + wh)$ where l = w = 5 cm and h = 3 cm. Both methods give the same answer.

What if the base wasn't square?

For a rectangular base, you'd need both length and width. The formula becomes $2(lw) + 2h(l + w)$ where the base area is lw instead of s².

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Calculate Surface Area: Cuboid with 25 cm² Base and 3 cm Height

Surface Area with Square Base Cuboid

❤️ 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

Why do I need to find the side length first?

How many faces does a cuboid have?

What's the difference between volume and surface area?

Can I use a different formula?

What if the base wasn't square?

🌟 Unlock Your Math Potential

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