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Gyaan Maths
CBSE · Class 6-12
Class 10 · Chapter 12

Surface Areas and Volumes

Formulas for combinations of solids: cube, cuboid, cylinder, cone, sphere and hemisphere.

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Mathematics · Class 10 (2026-27)
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Detailed theory
Cube (edge aa): TSA =6a2= 6a^2, volume =a3= a^3. Cuboid (l×b×hl\times b\times h): TSA =2(lb+bh+hl)= 2(lb + bh + hl), vol =lbh= lbh. Cylinder (r,hr, h): CSA =2πrh= 2\pi rh, TSA =2πr(r+h)= 2\pi r(r+h), vol =πr2h= \pi r^2 h. Sphere (rr): SA =4πr2= 4\pi r^2, vol =43πr3= \tfrac{4}{3}\pi r^3.
Key concepts & formulas
01
Volume of hemisphere =23πr3= \tfrac{2}{3}\pi r^3.
02
Frustum volume =13πh(r12+r22+r1r2)= \tfrac{1}{3}\pi h(r_1^2 + r_2^2 + r_1 r_2).
03
Combined solids: add or subtract carefully.
04
TSA cube =6a2= 6a^2; cuboid =2(lb+bh+hl)= 2(lb + bh + hl).
05
Volume of cylinder =πr2h= \pi r^2 h; cone =13πr2h= \tfrac{1}{3}\pi r^2 h.
06
TSA of cylinder =2πr(r+h)= 2\pi r(r + h); sphere =4πr2= 4\pi r^2.
Gyaan Maths — CBSE Class 6-12, built for board-toppers.
v1.1 · Sept 2026