# Chapter 10

### Michael S.

## Formula's

## Area of a Parallelagram

A=b*h

## Area of a Trapoziod

A=1/2(b+b)h

## Area of a Circle

A=π*r*r

## Surface Area of a Prism

S=2B+Ph

## Surface Area of a Cylinder

S=2πr*r+2πrh

## Surface Area of Pyramid

S=B+1/2*Plt

## Surface Area of a Cone

S=πr*r+πrl

## Surface Area of a Sphere

S=4πr*r

## Volume of a Prism

V=Bh V=lwh

## Volume of a Cylinder

V=Bh V=πr*rh

## Volume of a Pyramid

V=1/3Bh

## Volume of a Cone

V=1/3*Bh 1/3(πr*r)h

## Volume of a Sphere

V=4/3*πr*r

**Symbol meanings**

**B**=Area of the base

**h**=Hight

**r**=Radius

**w**=Width

**V**=Volume

**l**=Slant hight

**P**=Perimiter

**b**=Base

## Chapter 10/1 Areas of Parallelograms and Trapezoids

## Vocabulary

**Base of a Parallelogram**- the length of any one of its sides.

**Height of a Parallelogram**- the perpendicular distance between the bases.

**Bases of a trapezoid**- Its two parallel sides.

**Height of a trapezoid**- the perpendicular distance between the bases.

## Chapter 10/2 Area of Circles

## Vocabulary

**Circle**- the set of all points in a plane that are the same distance from a fixed point called the center.

**Radius**- the distance from the center to any point of the circle.

**Diameter**- the distance across the circle through the center.

**Circumference**- the distance around the circle/perimeter.

## How to find circumference

r=11

C=2πr

2*3.14*11

C=69.08

C=2πr

2*3.14*11

C=69.08

## Chapter 10/3 Three-Dimensional Figures

## Vocabulary

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

**Polyhedron**- a solid that is enclosed by polygons.

**Faces**- the polygons that form a polyhedron.

**Prism**- a polyhydron with two congruent bases that lie in parallel and the other rectangular faces.

**Pyramid**- a polyhydron with one base and triangular sides(faces).

**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 a space that are the same distance from a fixed point called the center.

**Edges**- segments where the faces of a polyhedron meet.

**Vertex**- a point where three or more edges meet.

## Chapter 10/4 Surface Areas of Cylinders and Prisms

## Vocabulary

**Net**- a two-dimensional pattern that forms a solid whin folded.

**Surface Area**- the sum of the areas of its faces.

## Chapter 10/5 Surface Areas of Cones and Pyramids

## Vocabulary

**Slant Height**- the hight of the lateral face, any face exept the base.

## How to Find Slant Hight

First make the object two-dimensional. Then you can see the hight and the length of the base. Divide the base in half. You need to find the hypotenuse of the triangle that those two parts make. The hypotenuse is the slant height. You use the pathagorean therum a²+b²=c² to figure out the hypotenuse. The answer to that will give you the slant hight of a pyramid or cone.

## Chapter 10/6 Volumes of Prisms and Cylinders

## Vocabulary

**Volume**- a measure of the amount of space it occupies.

## Real Life Situation

You want to fill in a wood pecker hole on your house. You need to find the volume of the cylinder shaped hole. The depth of the hole is 2 cm, the height of the hole is 4 cm. Find the volume of the wood that will be able to plug the hole.

V=π(r*r)*h

V=π(2*2)*2

V=π*4*2

V=25.12 cm cubed

V=π(r*r)*h

V=π(2*2)*2

V=π*4*2

V=25.12 cm cubed

## Chapter 10/7 Volumes of Pyramids and Cones

## Vocabulary

**Pyramid**- a polyhedron with one base and the other faces are triangles.

**Cone**- a solid with one circular base.

**Volume**- a measure of the amount of space it occupies.