Mensuration (Areas and Volumes) • Topic 3 of 3

Surface Area and Volume of Cylinder and Cone

What are Cylinder and Cone?

  • Cylinder: A 3D solid with two parallel circular bases connected by a curved surface
  • Cone: A 3D solid with a circular base and a curved surface tapering to a point (vertex)

Right Circular Cylinder (radius = r, height = h):

MeasurementFormula
Total Surface Area (TSA)\(2\pi r(r + h)\)
Volume\(\pi r^2 h\)

Right Circular Cone (radius = r, height = h, slant height = l):

MeasurementFormula
Curved Surface Area (CSA)\(\pi r l\)
Total Surface Area (TSA)\(\pi r(r + l)\)
Volume\(\frac{1}{3} \pi r^2 h\)

Important Notes:

  • π ≈ 3.14 or 22/7
  • CSA is also called lateral surface area
  • For cone, l (slant height) is NOT the same as h (vertical height)
Volume FormulasCuboidl × b × hCubeCylinderπr²hCone(1/3)πr²hSphere(4/3)πr³Hemisphere(2/3)πr³Unit Conversions:1 m³ = 1,000,000 cm³1 litre = 1000 cm³ = 1 dm³1 m³ = 1000 litresCone volume = (1/3) × Cylinder volume (same base & height)Sphere volume = (2/3) × Cylinder volume (same radius & height=2r)
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Worked Example

Solve a standard problem on Surface Area and Volume of Cylinder and Cone.

Solution

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

Key Points

  • Understand the definition and properties of Surface Area and Volume of Cylinder and Cone.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Tap an option to check your answer0 / 4
Q1.The volume of a cylinder is:
Explanation: $\pi r^2 h$.
Q2.The curved surface area of a cylinder is:
Explanation: $2\pi r h$.
Q3.The volume of a cone is:
Explanation: $\tfrac13\pi r^2 h$.
Q4.The slant height of a cone is:
Explanation: $l=\sqrt{r^2+h^2}$.