Class 10 · Chapter 12

Surface Areas and Volumes

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

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Detailed theory

Cube (edge

a

): TSA

= 6a^2

, volume

= a^3

. Cuboid (

l\times b\times h

): TSA

= 2(lb + bh + hl)

, vol

= lbh

. Cylinder (

r, h

): CSA

= 2\pi rh

, TSA

= 2\pi r(r+h)

, vol

= \pi r^2 h

. Sphere (

r

): SA

= 4\pi r^2

, vol

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

Key concepts & formulas

Volume of hemisphere

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

Frustum volume

= \tfrac{1}{3}\pi h(r_1^2 + r_2^2 + r_1 r_2)

Combined solids: add or subtract carefully.

TSA cube

= 6a^2

; cuboid

= 2(lb + bh + hl)

Volume of cylinder

= \pi r^2 h

; cone

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

TSA of cylinder

= 2\pi r(r + h)

; sphere

= 4\pi r^2