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MGF1106
Unit Three Ex. 5.6 Three Dimensional Figures,
Volume and Surface Area Objectives 30-36
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Exercise 5.6
Objective 30
To find the surface area of a rectangular solid
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Rectangular solid
l length, w width,h height
Surface area
2l w 2wh 2l h
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Find the surface area of a rectangular solid that
is 12 cm by 5 cm by 6 cm.
A 2l w 2l h 2wh
A 2(12)(5) 2(12)(6) 2(5)(6)
324 cm2
A 120 144 60
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Exercise 5.6
Objective 31
To find the volume of a cylinder
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Cylinder
V ? r2h
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Find the volume of a cylinder with height of 8 cm
and a base whose radius is 4 cm.
V ? r2h
V ? (4)2(8)
V ?(16)(8)
V 128? cm3
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Exercise 5.6
Objective 32
To find the volume of a cone
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Cone
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Find the volume of a cone that is 20 meters high
and has a base with radius of 4 meters.
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Exercise 5.6
Objective 33
To find the volume of a sphere
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Sphere
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Find the volume of sphere of radius 4 feet.
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Exercise 5.6
Objective 34
To find the volume of a rectangular solid
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Rectangular solid
l length, w width,h height
V lwh
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Find the volume of a rectangular solid that is 12
cm by 5 cm by 6 cm.
V l w h
V 12(5)(6)
V 360 cm3
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Exercise 5.6
Objective 35
To find the volume of a pyramid
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Pyramid
h height drawn perpendicular to the base
B area of base
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Find the volume of a pyramid of height 12 cm and
the base is a rectangle 7 cm by 8 cm.
Find B, the area of the base.
B (7)(8)
B 56 cm2
V 4(56)
V 224 cm3
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Exercise 5.6
Objective 36
To solve real problems involving the surface area
or volume of a three dimensional figure
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If the length of each side of a cube is tripled,
what effect does this have on the volume?
V x3
V (3x)3
V 27x3
Volume is multiplied by 27.
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If the length of each side of a cube is tripled,
what effect does this have on the surface area?
A 6x2
A 6(3x)2
A 6( 9x2 )
A 54x2
The surface area is multiplied by 9.
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A bale of hay measures 3 feet by 4 feet by 8
feet. A flatbed truck can carry 20 bales of hay.
What is the total volume of hay carried on the
truck?
Step 1 Find the volume of one bale.
V 3 x 4 x 8
V 96 ft3
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Step 2 Find the total volume by multiplying
the number of bales by the volume of one bale.
Total Volume 20(96)
1920 ft3
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How many 6-ounce cups of ice cream can be served
from a container that is 5.25 inches in diameter
and 11.25 inches high? (1 ounce 1.9 cubic
inches)
Step 1 Find the volume of the container.
V ? r2h
V ? (2.625)2(11.25)
V 243.535 in3
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V 243.535 in3
Step 2 Find the number of ounces in the
container.
128.1763158 ounces
Step 3 Find the number of servings.
21.3617193 cups
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A storage tank has a diameter of 20 inches and is
6 feet tall. The shape of the tank is a right
circular cylinder. How many gallons will it
hold? (7.5 gallons 1 cubic foot)
Step 1 Find the volume of the tank.
V ? r2h
d 20 in
r 10 in
Change 10 in to feet
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V ? r2h
V 13.08996939 ft3
Step 2 Find the number of gallons.
Number of gallons
98.17477042 gal