Volume_art.jpgThe volume of an object is the measure of the amount of three dimensional space it takes up.

The volumes and surface areas of certain simple objects such as cubes and prisms can be calculated using formulae.

The surface area of an object is the total area of the outside surfaces of the object.

Volume and Surface Area Formulae
Units of Volume

 

 

Units of Volume

  • The basic unit for volume is the cubic metre, written m3.
  • 1 cubic metre is the volume occupied by a cube of length 1 metre.
  • Smaller volumes are often measured in cubic centimetres, cm3, sometimes called cc.
  • 1 litre = 1000 cm3
    1 mL = 1 cm3 (1 cc)

Volume and surface area formulae

Only the cube and cuboid formulae need to be memorised. 

 

Solid
Name
Volume
Surface Area
Year_10_Volume_01.gif

Cube

V = l × l × l

= l3

S = 2l2+ 2l2+ 2l2

= 6l2

Year_10_Volume_02.gif

Cuboid or

Rectangular

Prism

V = (shaded area) × l
= (b × h) × l
= bhl

S = 2bh + 2hl + 2bl

Year_10_Volume_03.gif
Triangular

Prism

Year_10_Volume_08.gif

 

S = bl + al + cl + bh

Year_10_Volume_04.gif

Cylinder
 

Year_10_Volume_09.gif

 

Year_10_Volume_13.gif

Year_10_Volume_05.gif

Pyramid

Year_10_Volume_10.gif

S = sum of areas of

each face

Year_10_Volume_06.gif
Cone
 

Year_10_Volume_11.gif

Year_10_Volume_14.gif
Year_10_Volume_07.gif
Sphere
Year_10_Volume_12.gif
Year_10_Volume_15.gif

 

 Try this useful activity on the volume and surface area of cuboids and triangular prisms

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