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Grade 9:  The Learning Equation Math

31.07 Surface Area and Volume

3icon.gif (4368 bytes)

Measurement

Refresher pp 70-1

 

SeekAWord2ech.class Author

Prerequisite Skills:

volume, area, surface area, pyramid, prism, cylinder

             

   

Learning Outcomes:

The student will:

 

Study the surface area and volume for the prisms, pyramids, cylinder and cone provided.

Link: LearnAlberta

 

Geometric Shape

Surface Area

B = area of the base

P = perimeter of the base

Volume

B = area of the base

P = perimeter of the base

prism (general)

  • B = area of base
  • P = perimeter of base
  • h = height

 

  SA = 2B + Ph V = Bh

triangular prism

  • a = altitude
  • b = base
  • h = #height

 

  SA = 2B + Ph

SA = 2(1/2ab) + (b + c + d)h

SA = ab + (b + c + d)h

triangular_prism_sml.png (33744 bytes)

V = Bh

V = 1/2 abh

triangular_prism.gif (1150 bytes)

rectangular prism

  • l = length
  • w = width
  • h = height

 

SA = 2B + Ph

SA = 2(lw) + (2l + 2w)h

rectangular_prism_net.gif (1694 bytes)

V = lwh

rectangular_prism.gif (1540 bytes)

Regular square prism

  • s = side length
  • h = height

 

SA = 2B + Ph

SA = 2(s2) + (4s)h

square_prism_sml.png (32923 bytes)

V = Bh

V = s2h

square_prism_vol.png (28523 bytes)

regular pentagonal prism

  • a = apothem length
  • s = side length
  • n = #sides
  • h = height

 

 

SA = 2B + Ph

SA = 2(1/2ans) + nsh

SA = 2(1/2a)(5)s + 5sh

SA = 5as + 5sh

pent_net.gif (1423 bytes)

V = Bh

V = 1/2ansh

V = 1/2a(5)sh

V = 5/2ash

pentagonal_prism.gif (1269 bytes)

regular hexagonal prism

  • a = apothem length
  • s = side length
  • n = #sides
  • h = height

 

 

SA = 2B + Ph

SA = 2(1/2ans) + nsh

SA = 2(1/2a)(6)s + 6sh

SA =6as + 6sh

hex_net.gif (1832 bytes)

V = Bh

V = 1/2ansh

V = 1/2a(6)sh

V = 3ash

hexagonal_prism.gif (1406 bytes)

cube

  • s = side length

 

SA = 2B + Ph

SA = 2(s2) + (4s)s = 6s2

cube_net_sml.png (28862 bytes)

V = Bh

V = s3

cube.gif (1355 bytes)

regular pyramid (general)

  • B = area of base
  • s = side length
  • l = slant heigth

 

SA = B + n(1/2sl)

l = slant height

V = 1/3Bh

regular triangular pyramid

  • a = apothem length
  • s = side length
  • n = #sides
  • l = slant height
  • h = height

 

SA = B + n(1/2sl)

SA = 1/2as + (3)(1/2sl)

SA = 1/2as + 3/2sl

triangular_reg_pyramid_sml.png (40438 bytes)

l = slant height

V = 1/3Bh

V = 1/3(1/2 ab)h

V = 1/6 abh

tpyramid.gif (2377 bytes)

 

regular square pyramid

  • s = side length
  • n = #sides
  • l = slant height
  • h = height

 

 

SA = B + n(1/2sl)

SA = s2 + (4)(1/2sl)

SA = s2 + 2sl

square_pyramid_sml.png (37371 bytes)

l = slant height

V = 1/3Bh

V = 1/3(b2)h

= 1/3b2h

spyramid2.gif (2815 bytes)

regular pentagonal pyramid

  • a = apothem length
  • s = side length
  • n = #sides
  • l = slant height
  • h = height

 

 

SA = B + n(1/2sl)

SA = 1/2a(5)s + (5)(1/2sl)

SA = 5/2as + 5/2sl

pentagonal_pyramid.gif (2204 bytes)

l = slant height

V = 1/3Bh

V = 1/3(1/2anb)h

V = 1/6 anbh

pentagonal_pyramid_vol.png (29199 bytes)

regular hexagonal pyramid

  • a = apothem length
  • s = side length
  • n = #sides
  • l = slant height
  • h = height

 

 

SA = B + n(1/2sl)

SA = 1/2a(6)s + (6)(1/2sl)

SA = 3as + 3sl

hexagonal_pyramid_sml.png (40635 bytes)

l = slant height

V = 1/3Bh

V = 1/3(1/2anb)h

V = 1/6 anbh

hexagonal_pyramid_vol.png (28342 bytes)

cylinder

  • B = area of base
  • P = perimeter of base
  • r = radius of circle
  • h = height

 

 

SA = 2B + Ph

SA = 2(π r2) + (2πr)h

cylinder_net_sml.png (33177 bytes)

V = Bh

V = π r2h

cylinder.GIF (1709 bytes)

cone

  • B = area of base
  • r = radius of circle
  • h = height

 

SA = πrs + πr2

cone_sml.png (34352 bytes)

Explanation

V = 1/3 Bh

V = 1/3πr2h

cone.png (38273 bytes)

The volume of a cone is one third the volume of the corresponding cylinder.

sphere

r = radius of circle

SA = 4πr2

sphere.GIF (3975 bytes)

V = 4/3πr3

sphere_volume.gif (1432 bytes)

 

Prism

hexagonal_prism.gif (1406 bytes)

V = Bh

Pyramid

hexagonal_pyramid_vol.png (28342 bytes)

V = 1/3 Bh

The volume of a pyramid is one third the volume of the corresponding prism.

Cylinder

cylinder.GIF (1709 bytes)

V = Bh

Cone

cone.png (38273 bytes)

V = 1/3Bh

The volume of a cone is one third the volume of the corresponding cylinder.

 

Review:

Areas and Volumes (use TAB key to move to the next answer)
(This page should be different each time you load it)
1. Answer =
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source:  Interactive sums

 

Enrichment:

 

 

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