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Name
Module #1:
Date
Worksheet 5c:
Total Surface Area & Volume of Prisms
View Tutorial 5c
³Objective: Find the lateral area, total surface area, and volume of rectangular
prisms.
A prism is a polyhedron with two congruent & parallel bases.
The other faces are the lateral faces. A prism is named for the shape of its
bases.
Base:
The shaded faces are called bases. Bases lie in parallel
planes and are congruent polygons.
Lateral Faces:The faces that are not bases are called lateral faces.
Lateral faces are parallelograms that intersect each other in
parallel segments called lateral edges.
Right Prisms: Prisms in which all lateral faces are rectangles, are called right prisms.
Altitude:
A segment joining the two base planes of a prism and perpendicular to both is an
altitude.
Height :
The length of an altitude is the height, h, of the prism.
Lateral Area: The lateral area (L.A.) of a prism is the sum of the areas of its lateral faces.
The lateral area of a right prism equals the perimeter (p) of the base
times the height of the prism.
L.A. = ph
Surface Area:The total area or surface area (S.A.) of a prism is the sum of the areas of all the
faces.
The surface area of a right prism equals the lateral area plus the area
(B) of both bases.
S.A. = L.A. + 2B
= ph + 2B
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Page 2 of 5
Module #1:
Worksheet 5c:
Name
Date
Total Surface Area & Volume of Prisms
Find the surface area of the right rectangular prism to the right.
Solution
S.A. = ph + 2B
= 2(l + w) •h + 2 (l •w)
8 cm
= 2(15 + 10)•8 + 2(15•10)
= 2(25)•8 + 2(150)
= 400 + 300
= 700
The surface area is 700 cm2
10 cm
15 cm
Find the surface area:
1.
2 cm
2.
11 cm
15 cm
4 cm
8 cm
7 cm
3. Find the surface area of a right rectangular prism that is 16 inches long, 14 inches wide,
and 7 inches high. First, draw the diagram.
Copyright 2000. All rights reserved.
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Page 3 of 5
Module #1:
Worksheet 5c:
Name
Date
Total Surface Area & Volume of Prisms
4. A customer wants you to estimate the cost of hanging wallpaper in a living room. Find the
cost for your company to hang wallpaper for the following diagram if your labor and
materials is $0.90 per square foot?
Though finding surface area is necessary to figure cost, the ceiling and the floor will not be
wallpapered, which are the 2 bases of the prism. How does the formula for surface area
change? *Hint: As you create the New Formula for the living room, think of the room as a prism
with the 2 bases missing (the floor & the ceiling).
S.A. = ph + 2B or
S.A. = 2(l+w)•h + 2 (l•w)
3’
New Formula without the 2 Bases
•
•
The height in the room is 9 feet.
Living
Room
19’x 21’
Use this and the measurement of the length and
width of the room in the diagram to calculate the
Surface Area without the 2 bases.
Total Surface Area of the room
without the 2 Bases
•
•
4’
4’
Each doorway is 7 feet high.
Use this and the widths of the doors given
in the diagram top, right to calculate the
surface area to be wallpapered
9’
*Hint: Doorways should be eliminated from
the total surface area to be wallpapered.
7’
7’
7’
Surface Area to
be wallpapered
×
Total surface area to be
wallpapered
Copyright 2000. All rights reserved.
=
Cost per
square foot
Total cost to wallpaper
the living room
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Page 4 of 5
Module #1:
Worksheet 5c:
Volume
Name
Date
Total Surface Area & Volume of Prisms
The volume of a right prism equals the area of a base times the
height of the prism.
V = Bh
Find the volume of the right rectangular prism to the right.
Solution
V = Bh
= l •w•h
= (15•10)•8
= 150•8
= 1200
The volume is 1200 cm3.
8 cm
10 cm
15 cm
Find the volume of the following right rectangular prisms:
5.
6.
7 cm
8 cm
11 cm
15 cm
12 cm
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89
Page 5 of 5
Module #1:
Worksheet 5c:
Name
Date
Total Surface Area & Volume of Prisms
7. Find the volume of a right rectangular prism whose dimensions are 11 cm by 15 cm
by 20 cm. First, draw the diagram.
8. Your supplier has quoted you a price of $50.00 per cubic yard for concrete. The labor
to excavate, build forms, and pour and smooth the concrete will be $25.00 per cubic
yard. Your customer would like to add a concrete patio to the backyard of his home,
what will it cost your company to add the patio with dimensions shown below?
*Hint: Notice the thickness(height) is given in inches and the other dimensions are givin in feet.
Express thickness (or height) as a portion of a foot. 9 inches is what portion of 12 inches?
9”
12’
18’
Volume of concrete
needed in feet
Volume of concrete
needed in yards
In the building trades concrete is sold by the cubic yard.
1 cubic yard contains 27 cubic feet since 1 yard = 3 feet.
So divide the volume in cubic feet by 27.
Cost of concrete patio including
labor and materials
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90