Unit 7: Solid Figures and Measurement

transcript

Unit 7: Solid Figures Unit 7: Solid Figures and Measurementand MeasurementNow’s the time to SHAPE UP!!Now’s the time to SHAPE UP!!

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

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.

Practice

http://www.thatquiz.org/tq-4/?-j20k0-la-n35-p0

Volume of cubes and rectangular prisms:

Volume and Surface Area mixed:

http://www.thatquiz.org/tq-4/?-j24u0-la-n35-p0

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?

V= Bh or l x w x hV= 6 x 5 or 3 x 2 x 5V= 30 m3

V = Bh or TTr2h

2 cm V = Bh or TTr2hV = 3.14 x 22 x 4V = 6.28 x 4 x 4V = 25.12 x 4 = 100.48 cm3

How do I find the volume for any

prism or cylinder?

V =Bh or l x w x h

Radius

Volume of a CylinderVolume of a Cylinder

Volume Height

Base Area

Radius

Base Areah

Base Area

V = Bh

B = r2

Find the volume of the cylinder to the nearest cubic unit.

Multiply and label correctly.

V 565.2 ft3

Replace with 3.14, r with 6, and h with 5.

V = Bh or r2h

V 3.14 62 5Write the formula.

V 3.14 36 5V 3.14 180

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.

2rB 2)5(B

2cm 25B

)10(25V3cm 250V

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

Practice

http://www.thatquiz.org/tq-4/?-j2800-la-n35-p0

Volume of Cylinders:

http://www.thatquiz.org/tq-4/?-j2cu0-la-n35-p0

Questions AnswersQuestions Answers

What is the formula for the volume of a

pyramid ?

What is the volume of a

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)

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)

4 cm 2 cm

Volume of a PyramidVolume of a Pyramid

V = ⅓Bh

Base Area

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?

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

Volume of a ConeVolume of a Cone

V = ⅓Bh

r B = r2

RadiusBase Area

What do you notice about the relationship between the volume of a cone and a

cylinder?

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

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.

)13)(36(31 V

2rB 26B

2m 36B

3m 156V

V = ⅓Bh

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

Practice

http://www.thatquiz.org/tq-4/?-j3000-la-n35-p0

Volume of Cones:

http://www.thatquiz.org/tq-4/?-j3cu1-la-n35-p0

Unit 7: Solid Figures and Measurement

Documents