Transcript Prealgebra & Introductory Algebra

8.3
Area, Volume, and
Surface Area
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Area Formulas
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Area Formulas
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Helpful Hint
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.
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Radius
r
Given a circle of radius, r, the circumference is C = 2πr.
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Area of a Circle
Dividing the circle into 4 equal sectors, half the circumference, πr, is blue and
the other half is red.
8 equal sectors
πr
πr
r
r
πr
πr
32 equal sectors
16 equal sectors
πr
πr
r
r
πr
πr
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Area of a Circle
64 equal sectors
128 equal sectors
πr
πr
r
r
πr
πr
2n equal sectors
Notice the rectangular shape.
πr
A = lw
A = (πr)r
r
πr
A = πr 2
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Plane Figures
Plane Figure
Drawing
Perimeter/
Circumference
P=a+b+c
Triangle
P=a+b+c+d
Parallelogram
P = 2l + 2w
Rectangle
P = 4s
Square
P=a+b+c+d
Trapezoid
C = πd or 2πr
Circle
Area
A=
1
bh
2
A = bh
A = lw
A = s2
A=
1
( B + b) h
2
A = πr 2
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Volume
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.
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Surface Area
A polyhedron is a solid formed by the intersection
of a finite number of planes.
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.
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Volume
The volume of a solid is the number of cubic units
in the solid.
1 centimeter
1 centimeter
1 centimeter
1 cubic centimeter
1 inch
1 inch
1 inch
1 cubic inch
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Rectangular Solid
height
width
length
Volume = length ∙ width ∙ height
V = lwh
SA = 2lh + 2wh + 2lw
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Cube
side
side
side
Volume = side ∙ side ∙ side
V = s3
SA = 6s3
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Sphere
radius
Volume = V = 4  r 3
3
SA = 4 r 2
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Circular Cylinder
height
radius
Volume = V = πr2h
SA = 2πrh + 2πr2
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Cone
height
radius
Volume = V = 1  r 2 h
3
SA =  r r + h +  r
2
2
2
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Square-Based Pyramid
height
side
1
Volume =  (side) 2  height
3
1 2
V= s h
3
B = area of base,
1
SA = B + pl p = perimeter,
2
l = slant height
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