Length:
- 1 Centimetre (cm) = 10 milimetre(mm)
- 1 Decimetre(dm) = 10 Centimetre
- 1 Metre = 10dm = 100 cm = 1000mm
- 1 Decametre (dam) = 10m = 1000cm
- 1 Hectometre (hm) = 10dam = 100m.
- 1 kilomemetre (km) =1000m = 100dam = 10hm.
- 1 Myriametre =10Kilometre
Area:
- 1cm^{2} =1 cm X 1cm= 10 mm X 10mm = 100 mm^{2}
- 1dm^{2} =1 dm X 1dm=10 cm X 10 cm =100 cm^{2}
- 1m^{2} = 1 m X 1 m = 10 dm = 10 dm = 100 dm^{2}
- 1 dam^{2} or 1are = 1 dam X 1dam = 10m X 10m = 100 m^{2}
- 1hm^{2} = 1 hectare = 1hm X 1hm = 100 m X 100 m = 10000 m^{2} = 100 dm^{2}
- 1km^{2} = 1 km X 1 km = 10 hm X 10 hm = 100 hm^{2} or 100 hectare
Volume:
- 1 cm^{3 }= 1 ml = 1 cm X 1 cm X 1 cm = 10 mm X 10 mm X 10 mm = 1000 mm^{3}
- 1 Litre = 1000 ml =1000 cm^{3}.
- 1 m^{3} = 1 m X 1 m X 1 m = 100 cm X 100 cm X 100 cm = 10^{6 }cm^{3} = 1000 litre = 1 kilolitre
- 1 dm^{3} = 1000 cm^{3}
- 1m^{3} = 1000 dm^{3}
- 1 km^{3} = 10^{9}m^{3}
Let there be cuboids of Length (l), Breadth (b), Height (h), Area (A) and Volume (V):-
If the length (l) of each edge, Area (A) and Volume (V) of a Cube:-
Radius (r), height (h), Area (A), and Volume (V) ;
- Lateral or Curved surface area= 2πrh = Product of Circumference of the circle and height
- Each Surface area = π r^{2}
- Total surface area of Right Circular cylinder= (2πrh + 2πr^{2}) = 2πr (h+r).
- Each Base surface area = π (R^{2}-r^{2}) {R= radius of outer cylinder, r=radius of inner cylinder).
- Lateral or Curved surface area of hollow cylinder= (External surface area) + (Internal surface area) = 2πRh + 2πrh = 2πh (R+r).
- Total surface area of hollow cylinder=2 π Rh+2 π rh=2 π ( R^{2}-r^{2} ) = 2πh (R+r) + 2π(R+r) (R-r) = 2π (R+r) (h+R-r)
- Volume of the cylinder =Measure of the space occupied by the cylinder=Product of the area of each circular sheet and height= π r^{2}h.
- Volume of a Hollow Cylinder = Exterior Volume –Interior Volume= π R^{2}h- π r^{2}h= π (R^{2}-r^{2})h
A Hollow Right Circular Cone of radius (r), height (h) and slant height (l), Area (A), Volume (V) then:
- Length of the circular edge=2 π r
- Area of the plane = π r^{2}
- Curved surface area of the cone= Area of the Sector
= 1|2 X (arc length) x ( radius)
=1|2 x 2πr x l = πrl.
= Half and (product of circumference of base) and (slant height)- Total surface area of the cone =Curved surface area + Area of the base. = π rl+ π r^{2}= π r (l+r).
- Volumes of a Right Circular Cone = 3 (Volume of the cone of radius r and height) = π r^{2}h=1/3 (π r^{2}) X h= 1/3 X (Area of the base) X (height).
Sphere is the radius r, Area (A) and Volume (V);
- Surface areas of a sphere: S = 4 π r^{2}.
- Curved surface area of a hemisphere: S = 2 π r^{2}.
- Total surface area of a hemisphere: S = 2 π r^{2}+ π r^{2}=3 π r^{2}
- If ‘R’ and ‘r’ are outer and inner radii of a hemisphere shell, then Outer surface area = 4 π R^{2}
- Volume of a sphere V = 4/3 X (π r^{3}).
- Volume of a hemisphere V = 2/3 X (π r^{3}).
- Volume of the spherical shell whose outer and inner radii and ‘R’ and ‘r’ respectively, V = 4/3 π(R^{3}-r^{3})