Chapter 10
Bristol M
10.1 Areas of Parallelograms and Trapezoids
Vocabulary:
Base of a parallelogram- the length of any of it's sides
Height of a parallelogram- perpendicular distance between the base and the opposite side
Bases of Trapezoids- are it's two parallel sides
Height of Trapezoids- perpendicular distance between the bases
Area of a Trapezoid
Area=1/2*(base1+base2)*height
Real Life Example of a Trapezoid
Extra Practice
=1/2(8+6)10 Substitute values 8 for b1, 6 for b2 and 10 for h
= 70 square centimeters
Area of a Parallelogram
Area=base*height
Real Life Example of a Parallelogram
Extra Practice
A=bh Write formula for area
=10.3(6.2) Substitute 10.3 for b & 6.2 for h
Answer:
63.86 square cenimeters10.2 Areas of Circles
Area- a flat, or plane figure is the number of unit squares that can be contained within it.
Circle- the set of points that are equidistant from a special point in the plane.
Radius- half a the diameter
Circumference- computed by multiplying the diameter by pi
Pi- It expresses the ratio of the circumference to the diameter of a circle
Area of a Circle
Area=3.14*radius to the power of 2
Real Life Example of a Circle
Extra Practice
=3.14(8)^2 Substitute 3.14 for pi and 8 for r
=200.96 square centimeters
10.3 Three-Dimensional Firgures
Solid- three-dimensional figure that encloses a part of space
Polyhedron- a solid that is enclosed by polygons
Face- that form a polyhedron
Prism- a polyhedron, 2 congruent bases that lie in parallel planes
Pyramid- polyhedron, one base
Cylinder- solid, with 2 congruent circular bases
Cone- solid, with 1 circular base
Sphere- solid, formed by all points in space that are the same distance
Edges- segments where faces of a polyhedron meet
Vertex- a point where three or edges meet
10.4 Surface Areas of Prisms and Cylinders
Net- two-dimensional pattern that forms a solid when it is folded
Surface Area- of a polyhedron is the sum of the areas of it's faces
Surface Area of a Prism
Surface area=2*Area of the base+base's perimeter*height
Real Life Example of a Prism
Extra Practice
=2(1/2*24*28)+ (7+24+28)7 Substitute B for the area of the type of prism. Add up all the sides for P.
= 1085 square units *No label put units*
Surface Area of a Cylinder
Surface area=2*area of the base+base's circumference*height
S=2pir^2+2pirh
Surface area=2*3.14*(radius) to the power of 2+2*3.14*(radius)*(height)
Real Life Example of a Cylinder
Extra Practice
=2*3.14(5)^2+2*3.14(5)(10) Substitute 5 for r and 10 for h
=471 square cenimeters
10.5 Surface Areas of Pyramids and Cones
Slant height- l of a regular pyramid is the height of a lateral face, that is, any face that is not the base
Surface Area of a Pyramid
Surface area=area of the base+1/2*base's perimeter*slant height`
Real Life Example of a Pyramid
Extra Practice
Find the perimeter of the base
P=8+8+8=24
S=B+1/2Pl Write formula for surface area of a pyramid27.7+1/2(24)(6) Substitute 27.7 for B, 24 for P and 6 for l
=99.7 square meters
Surface Area of a Cone
Surface area=3.14*(radius) to the power of 2+3.14*(radius)*(slant height)
Real Life Example of a Cone
Extra Practice
=3.14(4)^2+3.14(4)(5) Substitute 4 for r and 5 for l
=113.04 square centimeters
10.6 Volume of Prisms and Cylinders
Volume: a solid is a measure of the amount of space it occupies
measured in cubic units
Volume of a Prism
Volume=area of the base*height
For B= length*width
Real Life Example of a Prism
Extra Practice
=lwh
=10(5)(6) Substitute 10 for l, 5 for w and 6 for h
=300 cubic inches
Volume of a Cylinder
V=pir2h
Volume=area of base*height
Real Life Example of a Cylinder
Extra Practice
=pir2h
=3.14(8)^2(15) Substitute 8 for r and 15 for h
=3014.4 cubic centimeters
10.7 Volume of Pyramids and Cones
Pyramid- polyhedron, one base
Cone- solid, with 1 circular base
Volume- a solid is a measure of the amount of space it occupies
measured in cubic units
Volume of a Pyramid
Volume=1/3*area of the base*height
Real Life Example of a Pyramid
Extra Practice
=1/3(30^2)(15) Substitute 30^2 for b and 15 for h
=4500 cubic feet
Volume of Cone
Volume=1/3*area of the base*height=1/3*3.14*(radius) to the power of 2*height
Real Life Example of a Cone
Extra Practice
=1/3pir^2h
=1/3*3.14(6)^2(12) Substitute 6 for r and 12 for h
=144pi Simplify
=452.389 cubic feet
Volume of a Sphere
Volume=4/3*area of the base*height
Real Life Example of a Sphere
Extra Practice
=4/3*3.14(9.6)^3 Substitute 9.6 for r
=3704.09472 cubic meters
Defition of Formulas
B= area of the base
C=base's circumference
V=volume
A=area
S=surface area
l=slant height
r=radius
h=height
b=base, 2-dimensional
pi=3.14
Formulas
Area of a Trapezoid- A=1/2(b1+b2)h
Area of a Parallelogram- A=bh
10.2
Area of a circle- A=pi*r^2
10.3
No formulas
10.4
Surface Area of a Prism- S=2B+Ph
Surface Area of a Cylinder- S=2B+Ch
10.5
Surface Area of a Pyramid- S=B+1/2*P*l
Surface Area of a Cone- S=pi*r2+pi*r*l
10.6
Volume of a Prism- V=Bh
Volume of a Cylinder- V=Bh
10.7
Volume of a Pyramid- V=1/3*B*h
Volume of a Cone- V=1/3Bh=1/3pi*r^2*h
Extra
Volume of a Sphere- V=4/3*Bh
Volume of a Prism- V=Bh-----=lwh
Surface Area of a Sphere- A=4*pi*r^2