SURFACE AREA
Prisms and Cylinders
Section 6-2
Prism
• A polyhedron with two congruent
parallel bases
• Named by the shape of the bases
• The other faces are called lateral
faces
Prisms
• Altitude (height) – perpendicular
segment that joins the planes of the
bases
Right Prism – the lateral faces are
rectangles. All prisms are right unless
otherwise stated.
Prisms
Lateral Face
Bases
Lateral edge
Prisms
• Lateral Area (LA)
– Sum of the areas of the lateral faces
– Product of perimeter of base and height
• Surface Area (SA)
– Total area of the entire prism
– Sum of lateral area (LA) and Bases (B)
Prism Formulas
• LA = ph
• SA = LA + 2B
Area of the base
CYLINDERS
• Is like a prism but the bases are circles
• Altitude (height) – Perpendicular segment
that joins the planes of the bases
Cylinder Formulas
• Lateral Area (LA)– product of
circumference of the base and the
height. (soup can label)
• Surface Area (SA) – sum of the
lateral area and the area of the
bases.
Cylinder Formulas
• LA = πdh
• SA = LA + 2B
2
• SA = πdh + 2πr
Find LA and SA
Find LA and SA
Find LA and SA
Find LA and SA
Word Problem
• The wheel of steamroller is a cylinder
with a diameter of 5’ and width of 7.2’.
How many square feet does a single
revolution of the wheel cover
Word Problem
• The surface area of a cylinder is 80π in2,
the radius is 4 in. Find the height of the
cylinder.
Word Problem
• A cylindrical storage tank with a
radius of 15’ and height of 45’ is to be
painted. 1 gallon of paint will cover
100 square feet of surface. How
many gallons are needed for 2 coats
of paint.
Word Problem
• A right triangular prism has a
height of 5 cm, its base is an
equilateral triangle with a side
of 2 cm. Find the LA and SA