Knowledge organisers

Surface Area and Volume: CBSE Class 9 Maths knowledge organiser

Everything to know about surface area and volume on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Surface area: The total area of all the faces or curved surfaces of a solid.
Volume: The space a solid takes up, in cubic units.
Slant height: The distance from the vertex of a cone to a point on the edge of its base.

Key formulas

Cuboid; cube	\(2(lb+bh+hl),\ lbh;\) \(6a^2,\ a^3\)
Cylinder	\(\text{CSA}=2\pi rh,\) \(\text{TSA}=2\pi r(r+h),\) \(V=\pi r^2h\)
Cone, \(l=\sqrt{r^2+h^2}\)	\(\text{CSA}=\pi rl,\) \(\text{TSA}=\pi r(l+r),\) \(V=\tfrac13\pi r^2h\)
Sphere; hemisphere	\(4\pi r^2,\ \tfrac43\pi r^3;\) \(2\pi r^2\ (3\pi r^2\text{ total}),\ \tfrac23\pi r^3\)
\(1\text{ m}^3=1000\) litres; scale factor \(k\): areas × \(k^2\), volumes × \(k^3\)

Worked example

Find the curved surface area of a cylinder with radius \(7\) cm and height \(10\) cm (take \(\pi = \dfrac{22}{7}\)).

\(2 \times \dfrac{22}{7} \times 7 \times 10 = 440\) cm².

Common mistakes

Using the height \(h\) instead of the slant height \(l\) in \(\pi rl\), or \(l\) instead of \(h\) in the cone's volume.
Using the diameter as the radius.
Forgetting the flat face in the total surface area of a hemisphere (\(3\pi r^2\), not \(2\pi r^2\)).
Mixing m and cm, or cm³ and litres.

You should be able to…

Use the surface area and volume formulas for cuboids, cylinders, cones and spheres in one step.
Find a missing dimension, convert units and answer costing questions.
Answer multi-part questions on tents, tanks and domes, choosing the right area each time.
Work backwards from an area or a volume and use 'the volume stays the same' when a solid is recast.

The printable sheet

Surface Area and Volume knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Surface Area and Volume knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Sequences and Progressions · Exploring Algebraic Identities · Linear Equations in Two Variables · Coordinate Geometry · Introduction to Euclid's Geometry: Axioms and Postulates · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers