Chapter 10

Jade N.

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

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A=bh

A=(15)(10)

A=15*10

A=150 units squared

10-2

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*radius squared

A=pi*4 squared

A=pi*16

A=50.26548246

Round

A=50.3 or 16pi units squared

10-3

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
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Pyramids can have any shaped base as long as the sides are triangles. Have only one base.
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Cylinder
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Cone
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10-4

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

10-5

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

10-6

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

10-7

Vocabulary

  • no vocabulary

Volume of a Pyramid

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

Volume of a Cone

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

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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