Chapter 12: Surface Areas and Volumes

Mathematics · CBSE Class 10 · NCERT Solutions

📖 Chapter 12 — Surface Areas and Volumes (CBSE Class 10 Maths): Detailed notes — formulas for solids and how to combine them.

Chapter 12 — Surface Areas and Volumes

📦 1. Formula Table

Solid	Curved/Lateral SA	Total SA	Volume
Cube (side a)	4a²	6a²	a³
Cuboid	2h(l+b)	2(lb+bh+hl)	l·b·h
Cylinder (r,h)	2πrh	2πr(r+h)	πr²h
Cone (r,h,l)	πrl	πr(r+l)	⅓πr²h
Sphere (r)	—	4πr²	(4/3)πr³
Hemisphere (r)	2πr²	3πr²	(2/3)πr³

Cone slant height: l = √(r² + h²). Use π = 22/7 unless stated.

🧩 2. Combination of Solids

Surface area of a combined solid = sum of the exposed surface areas of each part (do NOT count the joined faces).
Volume of a combined solid = sum of the volumes of the individual parts.

🧠 Remember: Cylinder vol πr²h, CSA 2πrh. Cone vol ⅓πr²h, CSA πrl, l=√(r²+h²). Sphere 4πr²/(4/3)πr³. Hemisphere 2πr²/(2/3)πr³. Combined SA = only exposed surfaces; combined volume = sum of volumes.

⭐ Exam Tips: ① Learn the formula table. ② For surface area, add only the visible/exposed surfaces. ③ For volume, simply add the parts. ④ Find slant height l before cone CSA. ⑤ Keep π = 22/7 unless told otherwise.

Chapter 12: Surface Areas and Volumes