Chapter 10
Nolan W.
Chapter 10 Section 1
Areas of Parallelograms and Trapezoids
Rectangle Formula A=b * h A=area b=base h=height | Parallelogram Formula A= b* h | Trapezoid Formula A= 1/2(b1+b2)h b1= one of the parallel bases b2= the other parallel base |
Vocabulary
Height of a parallelogram- The perpendicular distance between the side whose length is the base and the opposite side.
Bases of a trapezoid- The lengths of the parallel sides sides of the trapezoid.
Height of a trapezoid- The perpendicular distance between the bases of the trapezoid.
Real Life Scenario
400 pieces of carpet
Chapter 10 Section 2
Areas of Circles
Formula for a circle
A= pi*r^2
pi= 3.14, pi button on calculator, or 22/7
r= radius
^2= squared
Formula for Circumference
Vocabulary
Circle- The set of all points in a plane that are the same distance, called the radius, from a fixed point, called the center.
Radius- The distance between the center and any point on the circle.
Diameter- The distance across the circle through the center.
Circumference- The distance around the circle.
Pi- The ratio of the circumference of a circle to its diameter.
Question
write the formula for circumference C= 2*pi*r
plug in the information you have 36.75=2*3.14*r
PEMDAS 36.75= 6.28r
multiplicative inverse property 36.75/6.28 =6.28r/6.28
solution 5.85=r
now write down formula for area of a circle A=pi*r^2
plug in info. A=3.14*5.85^2
PEMDAS & solution A=337.420161
Chapter 10 Section 3
Three-Dimensional Figures
Vocabulary
Polyhedron- A solid that is enclosed with polygons
Face- a polygon that is a side of the polyhedron
Prism- A solid, formed by polygons, that has two congruent bases lying in parallel planes
Pyramid- A solid, formed by polygons, that has one base. The base can be any polygon, and the other faces are triangles
Cylinder- A solid with two congruent circular bases that lie in parallel planes
Cone- A solid with one circular base
Sphere- A solid formed by all points in space that are the same distance from a fixed point called the center
Edge- A line segment where two faces of the polyhedron meet
Vertex- A point at which three or more edges of a polyhedron meet
Chapter 10 Section 4
Surface Areas of Prisms and Cylinders
Surface Area of a Prism Formula S=2B+Ph S= Surface Area B= AREA of the base P= Perimeter | Surface Area of a Cylinder Formula S=2B+Ch or S=2*pi*r^2+2*pi*r*h C=circumference | Net A two-dimensional representation of a solid. This pattern forms a solid when it is folded |
Vocabulary
Surface Area- The sum of the areas of the faces of the polyhedron
Chapter 10 Section 5
Surface Area of Pyramids and Cones
Vocabulary
Chapter 10 Section 6
Volumes of Prisms and Cylinders
Vocabulary
Question
Write the formula needed to solve V=Bh or V=l*w*h
substitute information you have 378= l*7*6
PEMDAS 378=l*42
multiplicative inverse property 9=l
solution 9in
Chapter 10 Section 7
Volumes of Pyramids and Cones
Vocabulary
Cone- A solid with one circular base
Volume- The amount of space the solid occupies
Bonus Lesson
Volume and Surface Area of a Sphere
Volume for a Sphere
V=4/3*pi*r^3
^3= to the third power
Surface Area of a Sphere
S=4*pi*4^2
Formulas
Every Formula from Chapter 10
Area of a Triangle- A=1/2*b*h
Area of a Parallelogram- A=b*hArea of a Trapezoid- A=1/2(b1+b2)h
Area of a Circle- A= pi*r^2
Surface Area of a Prism- S=2*B+P*h
Surface Area of a Cylinder- S=2*B+C*h or S=2*pi*r^2+2*pi*r*h
Surface Area of a Pyramid- S=B+1/2*P*l
Surface Area of a Cone- S=pi*r^2+pi*r*l
Surface Area of a Sphere- S=4*pi*r^2
Volume of a Prism- V=B*h
Volume of a Cylinder- V=B*h or V=pi*r^2*h
Volume of a Pyramid- V=1/3*B*h
Volume of a Cone- V=1/3*B*h or V=1/3*pi*r^2*h
Volume of a Sphere- V=4/3*pi*r^3