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Grade 8:  The Learning Equation Math

32.06 Surface Area

3icon.gif (4368 bytes)

3D Objects & 2D Shapes

Refresher pp 64-5

Learning Outcomes:

The student will:

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)

  SA = 2B + Ph V = Bh

triangular prism

  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

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

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

 

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

 

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

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)

SA = B + n(1/2sl)

l = slant height

V = 1/3Bh

regular triangular pyramid

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

 

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

 

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

 

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

SA = 2B + ph

SA = 2(π r2) + (2πr)h

cylinder_net_sml.png (33177 bytes)

V = Bh

V = π r2h

cylinder.GIF (1709 bytes)

 

Review:

Interactive sums - Areas and Volume

 

Enrichment:

 

Key Terms:

area, surface area, volume, right prism, triangular prism, rectangular prism, cube, cylinder, face, congruent, equilateral, net, prism

Prerequisite Skills:

 Area and Perimeter: Quadrilaterals and Circles:  Grade 8 Lesson 22.03

 Using the Pythagorean Relationship:   Grade 8 Lesson 32.02

Circle Problems:   Grade 7 Lesson 31.02

Substitutions and Relations:   Grade 8 Lesson 21.01

Area and Perimeter(Quadrilaterals and Circles):   Grade 8 Lesson 32.03

 

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Comments to:  Jim Reed
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