Correspondence Math 24 Surface Area and Volume

Math 20 Perimeter/Area Surface Area/Volume Pi Distributive Property Equations Equation Methods Factoring

You will focus on the Volume column for Alberta's Mathematics 24 Program. The pictures included in the Surface Area column will help you understand how the 3D object was created.

Geometric Shape

Surface Area

Enrichment

A = area of the base

P = perimeter of the base

Diagrams are Nets

Volume

A = area of the base

P = perimeter of the base

Diagrams are Skeletons

prism (general)

Base and Top match
Sides: rectangle

SA = 2A + Ph

V = Ah

triangular prism

Base: triangle
Top: triangle
Sides: rectangles

SA = 2A + Ph

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

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

triangular_prism_sml.png (33744 bytes)

V = Ah

V = 1/2 abh

rectangular prism

Base: rectangle
Top: rectangle
Sides: rectangles

SA = 2A + Ph

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

rectangular_prism_net.gif (1694 bytes)

rectangular_prism.gif (1540 bytes)

Regular square prism

Base: square
Top: square
Sides: rectangles

SA = 2A + Ph

SA = 2(s²) + (4s)h

square_prism_sml.png (32923 bytes)

V = Ah

V = s²h

square_prism_vol.png (28523 bytes)

regular pentagonal prism

Base: pentagon
Top: pentagon
Sides: rectangles

SA = 2A + Ph

SA = 2(1/2ans) + nsh

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

SA = 5as + 5sh

pent_net.gif (1423 bytes)

V = Ah

V = 1/2ansh

V = 1/2a(5)sh

V = 5/2ash

pentagonal_prism.gif (1269 bytes)

regular hexagonal prism

Base: hexagon
Top: hexagon
Sides: rectangles

SA = 2A + Ph

SA = 2(1/2ans) + nsh

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

SA =6as + 6sh

hex_net.gif (1832 bytes)

V = Ah

V = 1/2ansh

V = 1/2a(6)sh

V = 3ash

hexagonal_prism.gif (1406 bytes)

cube

Base: square
Top: square
Sides: squares

SA = 2A + Ph

SA = 2(s²) + (4s)s = 6s²

cube_net_sml.png (28862 bytes)

V = Ah

V = s³

cube.gif (1355 bytes)

regular pyramid (general)

Top: point
Sides: triangles

SA = A + n(1/2sl)

l = slant height

V = 1/3Ah

regular triangular pyramid

Base: triangle
Top: point
Sides: triangles

SA = A + n(1/2sl)

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

SA = 1/2as + 3/2sl

triangular_reg_pyramid_sml.png (40438 bytes)

V = 1/3Ah

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

V = 1/6 abh

tpyramid.gif (2377 bytes)

regular square pyramid

Base: square
Top: point
Sides: triangles

SA = A + n(1/2sl)

SA = s² + (4)(1/2sl)

SA = s² + 2sl

square_pyramid_sml.png (37371 bytes)

V = 1/3Ah

V = 1/3(b²)h

= 1/3b²h

spyramid2.gif (2815 bytes)

regular pentagonal pyramid

Base: pentagon
Top: point
Sides: triangles

SA = A + n(1/2sl)

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

SA = 5/2as + 5/2sl

pentagonal_pyramid.gif (2204 bytes)

V = 1/3Ah

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

V = 1/6 anbh

pentagonal_pyramid_vol.png (29199 bytes)

regular hexagonal pyramid

Base: hexagon
Top: point
Sides: triangles

SA = A + n(1/2sl)

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

SA = 3as + 3sl

hexagonal_pyramid_sml.png (40635 bytes)

V = 1/3Ah

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

V = 1/6 anbh

hexagonal_pyramid_vol.png (28342 bytes)

cylinder

Base: circle
Top: circle
Side: rectangle (label)

SA = 2A + Ph

SA = 2(p r²) + (2pr)h

cylinder_net_sml.png (33177 bytes)

V = Ah

V = p r²h

cylinder.GIF (1709 bytes)

cone

Base: circle
Top: point
Side: none (part of a circle)

cone_sml.png (34352 bytes)

Explanation

V = 1/3 Ah

V = 1/3pr²h

cone.png (38273 bytes)

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

sphere

Base: none
Top: none
Sides: none

SA = 4pr²

sphere.GIF (3975 bytes)

V = 4/3pr³

sphere_volume.gif (1432 bytes)

Comments to: Jim Reed