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8.3
Area, Volume, and Surface Area
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Area Formulas
Continued.
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Area Formulas
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Area is always measured in square units.
When finding the area of figures, check to make sure that all measurements are in the same units before calculations are made.
Helpful Hint
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r
Given a circle of radius, r, the circumference is C = 2π r.
Radius
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Area of a Circle
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Notice the rectangular shape.
A lw
A (πr)r
A πr 2
2n equal sectors
πr
πr
r
64 equal sectors
πr
πr
r
128 equal sectors
πr
r
πr
Area of a Circle
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P a b c
P a b c d
P 2l 2w
P 4s
P a b c d
Plane Figure DrawingPerimeter/ Circumference Area
Triangle
Parallelogram
Rectangle
Square
Trapezoid
Circle C π d or 2π r
A bh
A lw
A s2
A πr 2
=1
( )2
A B + b h
=1
2A bh
Plane Figures
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Volume measures the number of cubic units that fill the space of a solid. The volume of a box or can is the amount of space inside.
Volume can be used to describe the amount of juice in a pitcher or the amount of concrete needed to pour a foundation for a house.
Volume
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A polyhedron is a solid formed by the intersection of a finite number of planes.
Surface Area
The surface area of a polyhedron is the sum of the areas of the faces of the polyhedron.
Surface area is measured in square units.Surface area is measured in square units.
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The volume of a solid is the number of cubic units in the solid.
1 centimeter1 centimeter
1 centimeter
1 inch1 inch
1 inch
1 cubic centimeter 1 cubic inch
Volume
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Rectangular Solid
length
widthheight
Volume = length ∙ width ∙ height V = lwh
SA = 2lh + 2wh + 2lw
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Cube
sideside
side
Volume = side ∙ side ∙ side
V = s3
SA = 6s3
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Sphere
V =
4
3 r3
SA = 4 r2
Volume
radius
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Circular Cylinder
Volume
V πr2h
radius
height
SA 2πrh + 2πr2
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Cone
V =
1
3 r2h
Volume
radius
height
SA = r r2 + h2 + r2
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Square-Based Pyramid
height
side
B = area of base, p = perimeter, l = slant height
Volume = side) height 21(
321
3V s h
1
2SA B pl