NCERT Solutions Class 9 Maths Chapter 14 — Math of Space: Surface Area and Volume#
Chapter 14 (Ganita Manjari Part II) finds the surface areas and volumes of cuboids, cubes, cylinders, cones, pyramids, spheres and hemispheres, and uses them in real problems and guesstimates — sensible estimates made from reasonable assumptions.
| Solid | Surface area | Volume |
|---|---|---|
| Cuboid $l \times w \times h$ | $2(lw + wh + hl)$ | $lwh$ |
| Cube (side $a$) | $6a^2$ | $a^3$ |
| Cylinder | CSA $2\pi rh$; TSA $2\pi r(h + r)$ | $\pi r^2 h$ |
| Cone | CSA $\pi rl$; TSA $\pi r(l + r)$ | $\dfrac{1}{3}\pi r^2 h$ |
| Pyramid | sum of the face areas | $\dfrac{1}{3} \times \text{base area} \times h$ |
| Sphere | $4\pi r^2$ | $\dfrac{4}{3}\pi r^3$ |
| Hemisphere | CSA $2\pi r^2$; TSA $3\pi r^2$ | $\dfrac{2}{3}\pi r^3$ |
Exercises#
- Exercise Set 14.1 — Cubes and cuboids, packing, painted cubes, cuboids with a given surface area (8 questions)
- Exercise Set 14.2 — Cylinders: ratios, percentage change, recasting a cube into rods (5 questions)
- Exercise Set 14.3 — Cones: surface area, volume, caps, tents, a cone of water (9 questions)
- Exercise Set 14.4 — Spheres and hemispheres: ratios, percentage change, painting a dome (8 questions)
- End-of-Chapter Exercises — Guesstimates, Earth and planets, strings around the equator, the crow and the marbles (22 questions)
What you will learn#
- Surface area and volume of cubes and cuboids, including packing and painted-cube problems.
- Cylinders and cones: curved and total surface area, volume, and percentage change.
- Spheres and hemispheres, and pyramids.
- Guesstimates — sensible estimates from reasonable assumptions.
Read and revise#
- NCERT Class 9 Maths Chapter 14 (PDF) — the Ganita Manjari Part II chapter itself.
- All Class 9 Maths chapters from Ganita Manjari Part I and Part II.
Frequently asked questions#
How many exercises are in Class 9 Maths Chapter 14?
Four exercise sets — 14.1 (8 questions), 14.2 (5 questions), 14.3 (9 questions) and 14.4 (8 questions) — plus 22 end-of-chapter exercises. Every question is solved step by step here.
What is a guesstimate?
An estimate made from sensible assumptions when exact data isn’t available — for example, how many scoops of ice cream fit in a box. State your assumptions, then calculate.