# Chapter 10

## 10-1

Vocabulary

• Base of a parallelogram- the length of any one of its sides.
• Height of a parallelogram-the perpendicular distance between the base and the opposite side
• Bases of a trapezoid-its two parallel sides
• Height of a trapezoid-the perpendicular distance between the bases

## Area of a parallelogram

The area of a parallelogramis the product of the base and the height

A=bh

A=bh

A=(15)(10)

A=15*10

A=150 units squared

## 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 a radius, from a fixed point, called the center
• Radius-the distance between a center and any point on the circle
• Diameter-the distance through a circle through the center
• Circumference-the distance around a circle
• Pi-the ratio of the circumference of a circle to its diameter

## Area of a circle

A=pi*4 squared

A=pi*16

A=50.26548246

Round

A=50.3 or 16pi units squared

## Vocabulary

• solid- a 3D figure that encloses a part of space
• polyhedron-a solid that is enclosed by polygons-has only flat surfaces
• face-the flat surfaces of a 3D figure
• prism-has 2 congruent bases that lie in parallel planes, the other faces are rectangles
• pyramid- has 1 base, the other faces are triangles
• cylinder-has 2 congruent circular bases that lie in parallel planes
• cone-has one circular base
• spheres- formed by all points that are the same distance from a fixed point called the center-
• edge-the segments where faces of a polyhedron meet
• vertex-a point where 2 or more edges meet
Pyramids can have any shaped base as long as the sides are triangles. Have only one base.
Cylinder
Cone

Sphere

## Vocabulary

• Net-a 2D pattern that makes a solid when folded
• Surface area-the sum of polyhedron's areas of its faces

## Surface Area of a Prism

S=2B+Ph

B=5*6.5*1/2

B=16.25

S=2(16.25)+Ph

P=(8*6.5)+(5*8)+(8*6.5)

P=52+40+52

P=144

S=2(16.25)+(144)h

H=8

S=32.5+1152

S=1184.5cm squared

## Surface Area of a Cylinder

S=2B+Ch=2 pi r squared+2pirh

B=2 pi r squared

B=2(pi*5 squared)

B=2(78.5)

B=157

S=2(157)+Ch

C=2 pi r

C=2(15.7)

C=31.4

S=2(157)+(31.40)h

S=314+314

S=628 cm squared

on video go to 3:30 min
Cylinder Volume and Surface Area

## surface area of a cone

S=pi*r squared+pi*r*l

## Vocabulary

• Slant height-the height of a lateral face, a side that is not the base
S=B+1/2Pl ...................B=25 squared L=4 P=5

S=(25)+1/2*(5)*(4)

S=(25)+1/2*20

S=25+10

S=35 units squared

## Vocabulary

• Volume-the measure of the amount of space it occupies

## Volume of a prism

V=Bh

B=10*10*1/2

B=100*1/2

B=50

V=50*25

V=1,250 units cubed

## Volume of a Cylinder

V=Bh............B=pi*r squared

B=pi*2 squared

B=pi*4

B=12.6

V=12.6*4

V=50.4

## Vocabulary

• no vocabulary

V=1/3Bh

B=10*8

B=80

V=1/3*80*h

V=1/3*80*6

V=1/3*5,880

V=1,960 in cubed

V=1/3Bh

B=pi*r squared

B=pi*3 squared

B=pi*9

B=28.3

V=1/3*28.3*h

V=1/3*28.3*8

V=1/3*226.4

V=75.5 cm cubed

## Volume of a Sphere

V=4/3*pi*r cubed

V=4/3*pi*64

V=4/3*201.5

V=268.6 cm cubed

Volume of a Sphere