# Chapter 10

### Grant F

## 10.1- Area=^2 : Volume=^3: LABELS: cm,m,ft,in

Areas of parallelograms

**Height-** is a measure of a polygon or solid figure, taken as a perpendicular from the base of the figure and trapezoids

**Base-** or radix is the number of different digits that a system of counting uses to represent numbers

## ParallelogramThe area of the parallelogram is the the product of the base and the height A=b*h | ## TrapazoidA= 1/2*(b1+b2)*h *The area of the trapezoid is one half the product of the sum of the bases and the height A= 1/2*(b1+b2)*h .5 * 6 * (6+1) 3*7 21 | ## VocabularyBase of a parallelogram- The length of anyone of its sides. Height of a parallelogram-The perpendicular distance between the base and the opposite side Base of a Trapezoid- 2 parallel sides Height of a trapezoid- The perpendicular distance between the bases |

## Trapazoid

A= 1/2*(b1+b2)*h

*The area of the trapezoid is one half the product of the sum of the bases and the height

A= 1/2*(b1+b2)*h

.5 * 6 * (6+1)

3*7

21

## 10.2

## Area of a circleA=pi(3.14)*r2 pi times radius squared | ## Circlecircumference-2*pi*r A=(Pi/4)*D *The area is the product of pi and the square of the radius Example- A=pi * r^2 d= 10 3.14 * 5^2 78.5 | ## VocabularyArea-The surface of amount of material needed to cover the shape circle- radius, diameter, circumference pi-3.14 or 22/7 pi=3.14159265359 |

## Circle

circumference-2*pi*r

A=(Pi/4)*D

*The area is the product of pi and the square of the radius

Example-

A=pi * r^2 d= 10

3.14 * 5^2

78.5

## 10.3

Prism- 2 congruent bases that lie in parallel planes. another sides are rectangles

Pyramid-1base. all the other sides are triangles.

## cylinder, cone, spherecylinder-a solid with 2 congruent circular bases that connect with parallel lines. cone- a solid with 1 circular base sphere-solid formed by all points in space that are same distance from one point called center | ## vertices, faces, edgesvertices-each angular point of a polygon, polyhedron, or other figure/3 or more edges meet faces- surfaces of a solid objects Edges- where 2 surfaces meet F+V=E+2d | ## kinds of solidsprism-rectangular prism pyramid- rectangular pyramid cylinder-solid with 2 congruent circular bases that are parallel cone, -1 solid with one circular base sphere Polyhedron-a solid that is enclosed by polygons POLYGONS-a plane figure with at least three straight sides and angles, and typically five or more. ^ |

## cylinder, cone, sphere

cylinder-a solid with 2 congruent circular bases that connect with parallel lines.

cone- a solid with 1 circular base

sphere-solid formed by all points in space that are same distance from one point called center

## vertices, faces, edges

vertices-each angular point of a polygon, polyhedron, or other figure/3 or more edges meet

faces- surfaces of a solid objects

Edges- where 2 surfaces meet

F+V=E+2d

## kinds of solids

prism-rectangular prism

pyramid- rectangular pyramid

cylinder-solid with 2 congruent circular bases that are parallel

cone, -1 solid with one circular base

sphere

Polyhedron-a solid that is enclosed by polygons

POLYGONS-a plane figure with at least three straight sides and angles, and typically five or more.

^

## 10.4

## Surface area of a PrismS=2B+Ph The Surface area of a prism is the sum of twice the area of the base(B) and the product of the bases perimeter P and the height h. S=2B+Ph 2(1/2*10*12)+(13+13+10)*15 =660 | ## Surface area of a cylinder S=2B+Ch=2*pi*r^2+2*pi*r*h The surface area of a cylinder id the sum of twice the area of a base B and the product of the bases circumference C and the height h. | ## Vocabualry and extraNet-a two dimensional pattern that forms a solid when it is folded Surface area-The sum of the areas of its faces Triangular prism- find the sum of the areas of the two triangular faces and the 3 rectangular faces. |

## Surface area of a Prism

S=2B+Ph

The Surface area of a prism is the sum of twice the area of the base(B) and the product of the bases perimeter P and the height h.

S=2B+Ph

2(1/2*10*12)+(13+13+10)*15

=660

## Surface area of a cylinder

The surface area of a cylinder id the sum of twice the area of a base B and the product of the bases circumference C and the height h.

## 10.5

Surface areas of pyramids and cones

Surface area=Area of base+Number of triangles*area of each triangle

## surface area of a pyramid surface area is the area of the base B and one half the product of the base perimeter and the slant height l S=B=+1/2*P*l | ## surface area of a cone The surface area of a cone is the sum of the area of the circular base with radius r and the product of pi the radius of the base and slant height l S=pi*r^2+pi*r*l | ## extra Slant height - is the height of lateral face that is any face that is not the base S=B+1/2Pl S=27.7+1/2[24][6] 99.7 S=pi r2+ pirl Pi[4]2+4*9 163.4 |

## surface area of a pyramid

S=B=+1/2*P*l

## surface area of a cone

S=pi*r^2+pi*r*l

## 10.6

volume-the amount of space that a substance or object occupies, or that is enclosed within a container, especially when great

## Volume of a prism V=Bh Volume is the area of the base and the height | ## Volume of a cylinderV=Bh volume = π · r^2 · h The volume is the product of the area of the base times the height π*4^2*6 301.593 | ## extraB=area of the base P= perimeter of the base |

## 10.7

Volumes of pyramids and cones

## Cone and cylinderThe volume of a cone is related to volume of a cylinder. The cone is one third the volume of a cylinder with same base and height Same thing with prisms and pyramids | ## Volume of a coneV=1/3Bh V=1/3*pi*r^2*h Volume equals one third area of the base and the height | ## Volume of a pyrimidV=1/3*B*h Volume is one third, area of the base and the height |

## Cone and cylinder

The volume of a cone is related to volume of a cylinder. The cone is one third the volume of a cylinder with same base and height

Same thing with prisms and pyramids

## Sphere

V=^3

A=^2

## Formulas

Trapezoid area-A=1/2(b1+b2)h

Circle area-A=pi*r^2

Surface area of prism-SA=2B +Ph

Surface area of a cylinder-SA=2B+Ch : SA= 2*pi*r^2+2*pi*r*h

Surface area of a pyramid-SA=B+1/2Pl

Surface area of a cone-SA=Pi*r^2+pi*r*l

Volume of a prism-V=Bh

Volume of a cylinder-V=Bh : V=Pi*r^2*h

Volume of a pyramid-V=1/3*B*h

Volume of a cone-V=1/3*B*h : V=1/3*pi*r^2*h

Volume of a sphere-V=4/3*pi*r^3

Surface area of a sphere-SA=4*pi*r^2