Class 9 · Chapter 14

Math of Space: Surface Area and Volume

Surface areas and volumes of the standard solids — cuboid, cube, cylinder, cone, sphere, hemisphere.

Watch this chapter

Top CBSE tutorials for Math of Space: Surface Area and Volume

Curated video coming soon. For now, open the freshest CBSE-focused YouTube results — Magnet Brains, LearnoHub, Physics Wallah & more.

Read the full chapter

Ganita Manjari · Class 9 (2026-27)

Official NCERT PDF

Latest 2026-27 edition on ncert.nic.in

NCERT Book Portal

Browse every chapter of the latest book

CBSE Academic Portal

Official CBSE curriculum

Tip: NCERT updated the syllabus for 2026-27. The links above open the latest edition on the official portal — chapter titles and numbering may differ from the notes shown here.

Detailed theory

CSA is the curved lateral surface only. TSA adds the flat circular ends (for cylinder, cone, hemisphere). Cuboids/cubes have no curved surface, so LSA and TSA both make sense in the flat-face sense.

Key concepts & formulas

Cuboid: LSA

= 2h(l+b)

, TSA

= 2(lb + bh + hl)

, Volume

= lbh

Cube (side

a

): TSA

= 6a^2

, Volume

= a^3

Cylinder (radius

r

, height

h

): CSA

= 2\pi r h

, TSA

= 2\pi r (r + h)

, Volume

= \pi r^2 h

Cone (radius

r

, height

h

, slant

\ell = \sqrt{r^2 + h^2}

): CSA

= \pi r \ell

, TSA

= \pi r (r + \ell)

, Volume

= \tfrac{1}{3}\pi r^2 h

Sphere (radius

r

): SA

= 4\pi r^2

, Volume

= \tfrac{4}{3}\pi r^3

Hemisphere: CSA

= 2\pi r^2

, TSA

= 3\pi r^2

, Volume

= \tfrac{2}{3}\pi r^3