In this section we calculate the volume and surface area of 3D shapes such as cubes, cuboids, prisms and cylinders.
Cube  Volume = x³ Surface area = 6x² 

Cuboid  Volume = xyz Surface area = 2xy + 2xz + 2yz 

Cylinder  Volume = π r²h Area of curved surface = 2π rh Area of each end = π r² Total surface area = 2π rh + 2π r² 

Prism  A prism has a uniform crosssection Volume = area of cross section × length = A l 
Calculate the volume of the cuboid shown.
Calculate the surface area of the cuboid shown.
Surface area  = (2 × 4 × 18) + (2 × 4 × 5) + (2 × 5 × 18) 
= 144 + 40 + 180  
= 364 m² 
Calculate the volume and total surface area of the cylinder shown.
Volume  =  π r²h = π × 4² × 6 = 96 π 
=  301.5928947 cm³  
=  302 cm³ (to 3 significant figures) 
Area of curved surface  =  2π rh = 2 × π × 4 × 6 
=  48π  
=  150.7964474 cm² 
Area of each end  =  π r² = π × 4² 
=  16π  
=  50.26548246 cm² 
Total surface area  =  150.7964474 + (2 × 50.26548246) 
=  251.3274123 cm²  
=  251 cm² (to 3 significant figures) 
Note: From the working we can see that the area of the curved surface is 48π, and that the area of each end is 16π. The total surface area is therefore
48π + (2 × 16π)  = 80π = 251.3274123 cm² 
= 251 cm² (to 3 significant figures) 
Calculate the volume of this prism.
Area of end of prism  =  × 8 × 6 
=  24 cm² 
Volume of prism  =  24 × 10 
=  240 cm³ 