# Chapter 10

## 10.1

Are of parallelograms and trapaziods
Area of a trapezoid

Area of circles

## A=πr^2

Example:

A=πr^2

A=π x 6^2

A=π x 36

A= 3.14 x 36

A= 113.04

Real Life:

If you are trying to find the area of a circular mirror to put in your mirror you would first find the radius of the mirror and square it to then multiple it by π to find the area of your mirror. Most time 3.14 can be used for π

## Vocab

Area-the number of squared 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 of a circle- the distance between the center of any point on the circle

Diameter of a circle-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

Area of a Circle - MathHelp.com - Math Help

## 10.3

Three-Dimensional Figures

## Vocab

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

Polyhedron-a solid that is enclosed by polygons

Face-the polygons that form a polyhedron

Prism-a solid, formed by polygons, that has two congruent bases lying in a 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 lines

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 of a polyhedron-a line segment where two faces of the polyhedron meet

Vertex-the endpoint of the rays that form an angle

## 10.4

Surface Areas of Prisms and Cylinders

## 10.5

Surface Areas of pyramids and cones
How To Find The Total Surface Area Of A Cone: THE EASY WAY!

## 10.6

Volumes of prisms and cylinders
Volume of a Prism - MathHelp.com - Math Help

## 10.7

Volumes of pyramids, cones, and spheres

## Vocabulary

Sphere-a solid formed by all points in a space that are the same distance form a fixed point called the center

(THERE IS OTHER VOCAB FOR THIS SECTION THAT CAN BE FOUND IN PREVIOUS SECTIONS)

Volume of a Sphere - MathHelp.com - Math Help

## Formulas

Area of Parallelograms- A=bh

Area of Trapezoids- A=1/2(b1+ b2)h

Area of Triangles- 1/2bh

Area of Circles- A=πr^2

Circumference of Circles- 2πr

Surface Area of Prisms- S=2B+Ph

Surface Area of Cylinders- S=2B+Ch

Surface Area of Pyramids- S=B+1/2Pl

Surface Area of Cones- S= πr^2+πrl

Volume of Prisms- V=Bh

Volume of Cylinders- V=Bh

Volume of Pyramids- V=1/3

Volume of Cones- V= 1/3Bh

Volume of Cones- V=1/3Bh

Volume of Spheres- V= 4/3πr^3

## Reminders

UNITS

When you are working with Surface Area or just Area the answer is unit squared ex. cm^2

When you are working with Volume the answer is units cubed ex. cm^3

The surface area and volume for a sphere are the same...with differently squared units

REMEMBER that there are always two bases(make sure you are looking at the shape in the correct way)

Make sure to be plugging in the right mini formulas when working with Area of the Base and Perimeter of the Base

Be aware of when it is asking to use the actual pi button or 3.14. Also be aware of what number it tells you to round to if needed.

## Extra Formulas

These are formulas that you may or may not have to use.

Pentagon-A=1/4 x Squared root 5(5+2 squared root 5) a^2

hexagon-A=3 Squared root 3 / 2 x a^2