Class 9 · Chapter 11

Surface Areas and Volumes

Cuboid, cube, right circular cylinder, cone, sphere, and hemisphere: surface areas and volumes.

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Detailed theory

Cuboid: 6 rectangular faces. Volume

= l\cdot b\cdot h

. TSA

= 2(lb + bh + hl)

. Cube (special cuboid with

l=b=h=a

): volume

= a^3

, TSA

= 6a^2

. Diagonal of cuboid

= \sqrt{l^2+b^2+h^2}

; of cube

= a\sqrt 3

Key concepts & formulas

Cylinder: volume

= \pi r^2 h

; CSA

= 2\pi rh

; TSA

= 2\pi r(r+h)

Sphere: SA

= 4\pi r^2

; volume

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

Cone: volume

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

; CSA

= \pi r\ell

; slant

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

Cuboid: volume

= lbh

; TSA

= 2(lb+bh+hl)

Cube: volume

= a^3

; TSA

= 6a^2

Hemisphere: volume

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

; TSA

= 3\pi r^2