Unit 7: Solid Figures and Measurement
description
Transcript of Unit 7: Solid Figures and Measurement
Unit 7: Solid Figures Unit 7: Solid Figures and Measurementand MeasurementNow’s the time to SHAPE UP!!Now’s the time to SHAPE UP!!
March 17, 2011March 17, 20111) Write your homework in your agenda: 1) Write your homework in your agenda:
HWP workbook Lesson 10-7 and 10-8 HWP workbook Lesson 10-7 and 10-8 #2, 4, 6 on each page#2, 4, 6 on each page
2) Open your agenda to your behavior 2) Open your agenda to your behavior card. card.
3) Take out your surface area worksheet, 3) Take out your surface area worksheet, put your name on it and leave it on your put your name on it and leave it on your desk.desk.
VolumeVolumeWhat am I Learning Today?What am I Learning Today?
How will I show that I learned it?How will I show that I learned it?Determine the formula for finding the
volume of fundamental solid figuresCompute volume using formulas and
appropriate units of measureSolve application problems involving
volume
VocabularyVocabulary Volume: The number of cubic units needed Volume: The number of cubic units needed
to fill a given space. to fill a given space.
What exactly does this mean?What exactly does this mean?It takes 10 centimeter cubes to cover the bottom layer of this rectangular prism (5cm x 2cm).It will take 3 layers of 10 cubes each to fill the prism. It takes 30 cubes or (5cm · 2cm · 3cm).Volume is expressed in cubic Volume is expressed in cubic
units, so the volume of the prism units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cmis 5 cm · 2 cm · 3 cm = 30 cm33..
Volume of a Rectangular PrismVolume of a Rectangular Prism
Volume HeightBase Area
Base Area What is the shape of the base here?What is the shape of the base here?What is the formula for its area?What is the formula for its area?
(Remember the “Base Area” formula will be determined by the base shape.)(Remember the “Base Area” formula will be determined by the base shape.)
h V = Bh
B = l x w Replace the “B” with l x w
V = l x w x h
Radius
Volume of a CylinderVolume of a Cylinder
VolumeHeight
Base Area
Radius
Base Area
h
Base Area V = Bh
B = r2
What is the shape of the base here?What is the shape of the base here?What is the formula for its area?What is the formula for its area?
Replace the “B” with (r)2
V = r2h
Questions AnswersQuestions Answers
What is the formula for the volume of a rectangular prism ?
Use the formula V= Bh, where B is the area of the base, and h is the height.
What is the volume of a cylinder?
3 m
5 m
2 m
V= Bh or l x w x hV= 6 x 5 or 3 x 2 x 5V= 30 m3
V = Bh or TTr2h
4 cm
2 cm V = Bh or TTr2hV = 3.14 x 22 x 4V = 3.14 x 4 x 4V = 3.14 x 16 = 50.24 cm3
How do I find the volume for any
prism or cylinder?
V =Bh or l x w x h
Find the volume of the rectangular prism.
V = Bh or V = l x w x h Write the formula.
V = 29 • 12 • 16
V = 5,568 in3
16 in.
29 in.12 in.
Substitute the values.
l = 29 w = 12 h = 16V = 348 • 16Multiply and label correctly.
Finding the Volume of a CylinderFinding the Volume of a CylinderFind the volume of a cylinder with height 10 cm Find the volume of a cylinder with height 10 cm
and radius 5cm.and radius 5cm.
10 cm
5 cm
2rB 2)5(B
2cm 25B
)10(25V3cm 250V
V = Bh
V = Bh
Find which cylinder has the greater volume.
Cylinder 1:
V 3.14 (1.5)2 12V = r2h
V 84.78 cm3
Cylinder 2:
V 3.14 32 6V = r2h
V 169.56 cm3
Cylinder 2 has the greater volume because 169.56 cm3 > 84.78 cm3.
Now Try This!!Now Try This!!Find the volume of each figure.
1) Rectangular prism with length of 20 cm, width of 15 cm, and height of 12 cm.
2) Cylinder with radius = 3.2 ft, height = 6 ft
V =3,600 cm3
V = 192.92 ft3
March 17, 2011March 17, 20111) Write your homework in your agenda: 1) Write your homework in your agenda:
NONE NONE2) Open your agenda to your behavior 2) Open your agenda to your behavior
card. card. 3) Take out your HWP workbook, open to 3) Take out your HWP workbook, open to
p. 89 and 90 and leave it on your desk.p. 89 and 90 and leave it on your desk.
Volume of a PyramidVolume of a Pyramid
Volume HeightBase Area
V = ⅓Bh
Base Area
h
B = l x w
What is the shape of the base here?What is the shape of the base here?What is the formula for its area?What is the formula for its area?
(Remember the “Base Area” formula will be determined by the base shape.)(Remember the “Base Area” formula will be determined by the base shape.)
What do you notice about the relationship between the volume of a pyramid
and a prism?
Replace the “B” with l x w
V = 1/3 (l x w x h)
Volume of a ConeVolume of a Cone
Volume HeightBase Area
V = ⅓Bh
h
r B = r2
RadiusBase Area
What do you notice about the relationship between the volume of a cone and a
cylinder?
What is the shape of the base here?What is the shape of the base here?What is the formula for its area?What is the formula for its area?
Replace the “B” with (r)2
V = 1/3( r2h)
Questions AnswersQuestions Answers
What is the formula for the volume of a
pyramid ?
What is the volume of a
cone?
V= 1/3 Bh or 1/3 (l x w x h)V= 1/3 (8 x 3) or 1/3 (4 x 2 x 3)V= 1/3 (24) V = 8 cm3
V = 1/3 Bh or 1/3 (TTr2h)
4 cm
2 cm
V = 1/3 Bh or 1/3 (TTr2h)V = 1/3 (3.14 x 22 x 4)V = 1/3 (3.14 x 4 x 4)V = 1/3 (12.56 x 4)V = 1/3 (50.24)V = 16.746 cm3
V = 1/3 Bh or 1/3 (l x w x h)
3 cm
4 cm 2 cm
Find the volume of the pyramid.
V = 1/3 Bh or 1/3 (l x w x h)
V = 1/3 (14 • 10 • 19)
V = 1/3 (140 • 19)V = 1/3 (2660)V = 886.67 cm3
Finding the Volume of a ConeFinding the Volume of a ConeThe radius of the base of a cone is 6 m. The radius of the base of a cone is 6 m.
Its height is 13 m. Find the volume.Its height is 13 m. Find the volume.
m 6
)13)(36(31 V
2rB 26B
2m 36B
3m 156V
m 13
V = ⅓Bh
V = ⅓Bh
Find the volume of the cone.
V = 1/3 Bh or 1/3 (TTr2h)
V 1/3 (3.14 42 16)V 1/3 (3.14 16 16)V 1/3 (50.24 16)V 1/3 (803.84)
V 267.95 cm3
Now Try This!!Now Try This!!Find the volume of each figure.
1) Pyramid with a height of 4 m, a length of 2.5 m and width of 2 m.
2) Cone with diameter = 4 in, height = 6 in
V =6.67 m3
V = 25.12 in3