Everything Maths Grade 10

• A pyramid is a geometric solid that has a polygon as its base and sides that converge at a point called the
  apex. The sides are not perpendicular to the base.


• The triangular pyramid and square pyramid take their names from the shape of their base. We call a
  pyramid a “right pyramid” if the line between the apex and the centre of the base is perpendicular to the
  base. Cones are similar to pyramids except that their bases are circles instead of polygons. Spheres are
  solids that are perfectly round and look the same from any direction.


• Surface area formulae for right pyramids, right cones and spheres:
  
  
  • square pyramid:b(b+ 2h)
  
  
  • triangular pyramid:^12 b(hb+ 3hs)
  
  
  • right cone:r(r+hs)
  
  
  • sphere: 4 r^2
  
  
  
  


• Volume formulae for right pyramids, right cones and spheres:
  
  
  • square pyramid:^13 b^2 H
  
  
  • triangular pyramid:^13 ^12 bhH
  
  
  • right cone:^13 r^2 H
  
  
  • sphere:^43 r^3
  
  
  
  


• Multiplying one or more dimensions of a prism or cylinder by a constantkaffects the surface area and
  volume.

End of chapter Exercise 13 – 7:

1.Find the area of each of the shapes shown. Round your answer to two decimal places if necessary.

a)

15 cm

5 cm

b)

7 mm

c)

8 cm

14 cm

14 cm

Chapter 13. Measurements 457