Surface Areas and Volumes • Topic 2 of 3

Surface Areas and Volumes of Combined Solids

What are Combined Solids?

Combined solids are three-dimensional shapes made by joining two or more basic solids. Examples include:

  • A cylinder with a hemisphere on top (like a capsule)
  • A cone mounted on a cylinder (like a tent)
  • A cuboid with a cylindrical hole

How to Find Surface Area of Combined Solids:

  • Add the surface areas of the individual parts
  • Subtract the area of the faces that are joined (they are not exposed)

How to Find Volume of Combined Solids:

  • Simply add the volumes of the individual parts
  • No subtraction needed (volume is additive)

Common Combined Solids:

CombinationShapesApplications
Cone + CylinderCone on top of cylinderTents, ice cream cones
Cuboid + CylinderCuboid with cylindrical holePipes through blocks, bearings
Cone + HemisphereCone on hemisphereRocket nose cones, party hats
Surface Area & Volume — Cylinder & ConerrhhrlCylinderConeCSA2πrhπrlTSA2πr(r+h)πr(r+l)Volumeπr²h(1/3)πr²hSlant—l = √(r²+h²)
Solved Examples
1
Worked Example

Solve a standard problem on Surface Areas and Volumes of Combined Solids.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Surface Areas and Volumes of Combined Solids.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The volume of a combined solid equals:
Explanation: Add the volumes.
Q2.The curved surface area of a hemisphere is:
Explanation: $2\pi r^2$.
Q3.The total surface area of a solid hemisphere is:
Explanation: $3\pi r^2$.
Q4.The surface area of a combined solid uses only the ___ surfaces.
Explanation: Exposed surfaces.
Practice more MCQs → 📝 Assignment · 35 marks