Surface Areas and Volumes of Solids (3D Solids)

Right Prism

Right Prism

Right Prism

Right Prism

Lateral Surface Area (L.S.A.)=Perimeterofbase×height Total Surface Area (T.S.A.)=L.S.A.+2×Areaof base

Volume (V)=Areaofbase×height

Cuboid

Cuboid

Cuboid

Cuboid

L.S.A.=2(lh+bh)

T.S.A.=2(lh+bh+lb)

Volume(V)=lbh

Bodydiagonal(d)=l2+b2+h2

Cube

Cube

Cube

Cube

L.S.A.=4a2

T.S.A.=6a2

Volume(V)=a3

Bodydiagonal(d)=3a

Cylinder

Cylinder

Cylinder

Cylinder

CurvedSurfaceArea(C.S.A.)=2πrh

T.S.A.=2πrh+2πr2

Volume (V)=πr2h

Right Pyramid

Right Pyramid

Right Pyramid

Right Pyramid

L.S.A=12×PerimeterofBase×SlantHeight

T.S.A.=L.S.A.+Areaofbase

Volume(V)=12×Areaofbas×Height

Cone

Cone

Cone

Cone

C.S.A.=πrl

T.S.A.=πrl+πr2

Volume(V)=13πr2h

Slantheight(l)=(r2+h2)

Frustum of a cone

Frustum of a cone

Frustum of a Cone

Frustum of a cone

VolumeoftheOriginalConeVolumeoftheremovedCone=Vv=(Rr)3=(Hh)3=(Ll)3

Sphere

Surface Areas and Volume of Sphere

Sphere

Surface Areas and Volume of Sphere

C.S.A.=4πr2

T.S.A.=4πr2

Volume(V)=43πr3

Hemisphere

Surface Areas and Volume of Hemisphere

Hemisphere

Surface Areas and Volume of Hemisphere

C.S.A.=2πr2

T.S.A.=3πr2

Volume(V)=23πr3