Chapter 10

Nolan W.

Chapter 10 Section 1

Areas of Parallelograms and Trapezoids

Vocabulary

Base of a parallelogram- The length of any side of the parallelogram can be used as the base.

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

Micheal wants to re-floor his bedroom, his room is a 20 ft. by 20 ft. square room. If the carpet comes per square foot, how many pieces of carpet will Micheal need to buy?


400 pieces of carpet

Chapter 10 Section 2

Areas of Circles

Big image

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

2*pi*r

Vocabulary

Area- The number of square units covered by a figure.

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

Knowing that the circumference of the circle is 36.75cm. squared, what is the area of this circle? Use 3.14 for pi and round to the nearest hundredth if needed.


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

Solid- a three-dimensional figure that encloses a part of space

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

Faces, Edges, and Vertices

Chapter 10 Section 4

Surface Areas of Prisms and Cylinders

Vocabulary

Net- A two-dimensional representation of a solid. This pattern forms a solid when it is folded

Surface Area- The sum of the areas of the faces of the polyhedron

Chapter 10 Section 5

Surface Area of Pyramids and Cones

Vocabulary

Slant Height-The height of ant face that is not the base of a regular pyramid
Surface Area Pyramid + Finding Slant Height

Chapter 10 Section 6

Volumes of Prisms and Cylinders

Vocabulary

Volume- The amount of space the solid occupies

Question

If a tissue box has the volume of 378in. cubed and the height is 6in. while the width is 7in. what is its length of the box?


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

Pyramid- A solid, formed by polygons, that has one base. The base can be any polygon, and the other faces are triangles

Cone- A solid with one circular base

Volume- The amount of space the solid occupies

Bonus Lesson

Volume and Surface Area of a Sphere

Big image

Volume for a Sphere

Formula

V=4/3*pi*r^3

^3= to the third power

Surface Area of a Sphere

Formula

S=4*pi*4^2

Volume Of A Sphere

Formulas

Every Formula from Chapter 10

Area of a Triangle- A=1/2*b*h

Area of a Parallelogram- A=b*h

Area 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