Prisms
A prism - polyhedron (many faces, a cylinder is a special case of a prism)
- has two parallel faces (bases) that are the same
- has same cross-section throughout its length
- named by the shape of its base
length
cross section
Hexagonal prism
Prisms
• A cuboid is a prism whose six faces are all rectangles.
• A cube is a special case of a cuboid in which all six faces are squares.
Volume of Prisms
By stacking 2D areas,
we create volume (3D)
h
cross-section
area
Base Area
h
A
Base Area
The volume depends on the height of the stack
Volume prism = base area ⨉ height
= cross-section area ⨉ height
Surface Area
p148
• Sum of all areas on the outside. It is measured in
square units [unit2].
A tin can
SA = 2πr2 + 2πrh
Surface Area
p150
h
πrl
Cones
•
A cone is a special pyramid with a circular base. The length l is known as the
slant height. h is the vertical (perpendicular) height.
•
The curved surface of the cone can be opened out to form a sector of a
circle.
•
Curved surface area = π r l , and
•
ଵ
Volume =
ଷ
ଶ
area = πrl
area = πr2
Surface Area
Find the total surface area of a solid cone of radius 4 cm and vertical
height 3 cm.
Let the slant height of the cone be l cm.
3
ଶ
p148
Net (for Surface Area)
• A net is a two-dimensional shape (plan) which can be folded to
form a three-dimensional shape.
h
What is the total surface area of this solid wedge?
h
Draw a net of the solid:
What is the volume of this solid wedge?
base area × height = (5x12)/2 × 7 = 30 x 7 = 210 cm3
Triangle is the base of the prism.
Find the cost of a 6 m by 4 m rectangular garden shed (with no bottom)
that is 2 m high if the metal sheeting costs $15 per square metre.
More than one
NET configuration
possible