The whole method
No formula of its own
A combined solid is two familiar solids joined together.
↳ Add what you can touch.
📚 Chapter Learning Kit
Surface Areas and Volumes · Class 10 Mathematics
English 2 topics 116 leveled MCQs 44 flashcards 2 games Free
Shared by a Veda teacher · Generated with Veda AI · Sep 2026
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What the join hides
Two circles vanish
When a cone sits on a cylinder, the cone's base and the cylinder's top are pressed together.
↳ Never add the two TOTAL surface areas.
A consequence
Joining always shrinks it
Two faces disappear, so the combined solid has less surface than the two parts had apart.
↳ If your answer went up, something is wrong.
Volumes simply add
Nothing hides inside
A join has no thickness, so no space is lost when two solids are stuck together.
↳ Where surfaces subtract, volumes add.
Base area times height
The cylinder
↳ The simplest of the six.
A third of its cylinder
The cone
↳ The 1/3 is the most-forgotten symbol in the chapter.
📖 Smart notes
What you'll study, topic by topic
1
Surface Area of a Combination of Solids
Two familiar solids joined together make a new shape with no formula of its own. Its surface area is found by adding the parts you can still see — and leaving out the faces that were glued.
- A combined solid has NO formula of its own — add the visible parts.
- The two faces that were JOINED are hidden, so neither is counted.
- Curved surface of a cylinder $= 2\pi rh$; total $= 2\pi r(r + h)$.
~45 min · full explanation, examples & memory tricks in the app
2
Volume of a Combination of Solids
Volumes behave more simply than surfaces: nothing is hidden inside a solid, so you simply add. And when something is hollowed out, you subtract.
- Volume of a combined solid $=$ the SUM of the parts. Nothing is hidden.
- For a cavity, SUBTRACT the hollowed volume from the whole.
- Volume of a cylinder $= \pi r^2 h$.
~45 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
116 questions laddered from warm-up to topper-level, each with an explanation. A taste:
The surface area of a combined solid is found by
Beginner
A adding the two total surface areas
B subtracting the smaller from the larger
C adding the surfaces that remain visible
D multiplying the two areas
Show answer & explanation
adding the surfaces that remain visible
The joined faces are hidden.
When a cone is placed on a cylinder of the same radius, the surfaces that disappear are
Beginner
A the cone's curved surface
B the cone's base and the cylinder's top
C the cylinder's base
D nothing disappears
Show answer & explanation
the cone's base and the cylinder's top
They are pressed together at the join.
Joining two solids together makes the total surface area
Intermediate
A larger
B unchanged
C exactly double
D smaller than the two apart
Show answer & explanation
smaller than the two apart
Two faces are lost.
The curved surface area of a cylinder is
Beginner
A $\pi r^2 h$
B $2\pi rh$
C $2\pi r(r+h)$
D $\pi rh$
Show answer & explanation
$2\pi rh$
The side, rolled out flat, is a rectangle.
🃏 Flashcards
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