How to Easily Find the Surface Area and Volume of Combined Solids (A Simple Guide for Confused Students — From My Classroom Experience)

supriyamathtutor
Jan 9
3 min read

As a math tutor, I have taught thousands of students, and one topic I see students struggle with again and again is Surface Area of Combined Solids.

Many students tell me:

“Ma’am, volume is okay… but surface area confuses me!”

And honestly, I understand why.

When shapes are combined, students often feel:

Overwhelmed by the diagram
Confused about which faces to include
Unsure what to add and what to subtract

The good news?👉 Combined solids are not difficult — they just need the right thinking approach.

Let me share the exact method I teach my students that makes this topic clear and stress-free.

Step 1: Understand What “Combined Solids” Really Means

A combined solid is simply two or more basic solids joined together, such as:

Cube + cuboid
Cylinder + hemisphere
Cone + cylinder

📌 Important rule:

No new formula is required.

We only use formulas we already know.

Step 2: Volume Is the Easier Part (Most Students Don’t Realize This!)

I always tell my students:

“Volume is friendly — it never hides.”

How to find Volume of Combined Solids:

Split the solid into simple shapes
Find the volume of each part separately
Add all volumes

Example:

Cylinder + Hemisphere

Total Volume=Volume of Cylinder+Volume of Hemisphere

That’s it. No subtraction. No tricks.

Most students feel confident here once they practice 2–3 questions.

Step 3: Why Surface Area Feels So Confusing

This is where students usually get stuck.

I’ve seen many students:

Add all surface areas blindly
Forget that some faces are hidden
Include areas that should not be counted.

So I teach them ONE golden rule 👇

Step 4: The Golden Rule for Surface Area ⭐

Only count the surfaces that are visible from outside.

That’s it.If a surface is inside or attached, it should NOT be included.

Step 5: My 3-Step Method for Surface Area (Works Every Time)

Step 1: Draw or Imagine the Shape Clearly

Take a moment to see the solid. Ask yourself:

Which parts are touching?
Which surfaces disappear?

Step 2: Cross Out the Common Faces ❌

Where two solids touch each other:

That face becomes internal
Do not include it

📌 This is the step most students skip — and that’s where mistakes happen.

Step 3: Add Only the Remaining Outer Surfaces

Now add:

Curved surfaces
Top or bottom surfaces
Any face that is visible from outside

Step 6: A Small Tip I Always Give My Students 💡

Before writing formulas, I ask my students:

“If I paint this solid, where will the paint touch?”

If paint cannot touch it → don’t include it in surface area.

This simple imagination trick has helped so many students improve their accuracy.

Common Mistakes to Avoid ❌

Adding surface area before removing common faces
Mixing curved surface area and total surface area
Rushing without understanding the shape

Slow thinking = fewer mistakes.

Final Words from My Teaching Experience 💬

Over the years, I’ve noticed one thing clearly:

Students don’t struggle because they are weak in math —they struggle because no one taught them how to think visually.

Once students learn to:✔ Break the shape✔ Identify hidden surfaces✔ Use basic formulas confidently

Combined solids become one of the easiest chapters.

If you’re a student (or a parent reading this), remember:

Math is not about memorizing — it’s about seeing and understanding.

Supriya Suman

Math Tutor | 16+ Years of Teaching Experience

Nurturing Excellence in Math