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Unit 4: Circles and VolumeVocabulary Builder
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Polyhedra Euler’s Formula net
edge
Cross section
Vertex
Face Horizontal plane Vertical plane
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Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Formula for volume
Substitutionh = 9
Base is a right triangle, legs 3 and 4.2
Multiply
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Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
1
2
3
4
5
1
2
3
4
5
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Ratio
Similar
Proportion
Scale factor
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Lateral area
Volume
Linear dimensions
Surface area
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Unit 4: Circles and Volume4.7 Volume of Prisms
(Rectangular, Triangular, and Cylinders)
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Volume
cubic
congruent
Right rectangular prism bases
length widthheight
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Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
𝑉 = 𝑙𝑤ℎ
𝑉 = 10.5 × 8 × 12
𝑉 = 1008𝑐𝑚3
𝑉 = 𝑙𝑤ℎ
𝑉 = 15 × 5 × 3
𝑉 = 225𝑐𝑚3
𝑉 = 142.5𝑐𝑚3 𝑉 = 456𝑐𝑚3
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
height bases
multiply
base
height
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
𝑉 =7 × 18 × 35
2
𝑉 = 2205𝑚𝑚3
𝑉 =22 × 15.3 × 19
2
𝑉 = 3195.4𝑐𝑚3
Must find the height!
𝑥2 + 9.52 = 182
𝑥2 = 233.75
𝑥 = 15.3
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
𝑉 = 1925𝑚3 𝑉 = 120𝑚3
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Daily 5 Question Check for Understanding
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Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
capacity
area
height
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
𝑉 = 𝜋𝑟2ℎ
𝑉 = 𝜋(8.5)2(7)
𝑉 = 1588.9𝑚3
𝑉 = 𝜋𝑟2ℎ
𝑉 = 𝜋 4.5 2(8.5)
𝑉 = 540.7𝑐𝑚3
𝑉 = 125.7𝑚𝑚3
𝑉 = 18472.6𝑐𝑚3
𝑉 = 505.8𝜋 𝑉 = 172.1𝜋
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Vocabulary Builder
Volume of Cylinders
Volume of Rectangular and Triangular Prisms
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Unit 4: Circles and Volume4.8 Volume of Pyramid and Spheres
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
One-third
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
𝑉 =8 × 8 × 10
3
𝑉 = 213.3𝑖𝑛3
𝑉 =400 × 36
3
𝑉 = 4800𝑦𝑑3
𝑉 = 15𝑐𝑚3 𝑉 = 48𝑐𝑚3
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
height
slant
Pythagorean Theorem
𝑥2 + 52 = 132
𝑥 = 12
𝑉 =10 × 10 × 12
3𝑉 = 400𝑖𝑛3
𝑥2 + 6.52 = 12.82
𝑥 = 11
𝑉 =13 × 13 × 11
3𝑉 = 619.7𝑚𝑚3
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
𝑥2 + 0.62 = 2.82
𝑥 = 2.73
𝑉 =1.2 × 1.2 × 2.73
3𝑉 = 1.3𝑐𝑚3
𝑥2 + 2.52 = 14.22
𝑥 = 13.9
𝑉 =5 × 5 × 13.9
3𝑉 = 116.5𝑚3
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Cones
One-third
circle
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
𝑉 =𝜋(7)2(24)
3
𝑉 = 1232𝑓𝑡3
𝑉 = 392𝜋
𝑉 =𝜋(4)2(12)
3
𝑉 = 201𝑚3
𝑉 = 64𝜋
𝑉 = 98𝑖𝑛3 𝑉 = 5131.3𝑚3
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Center
radius
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Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
𝑉 =4𝜋(5)3
3
𝑉 = 523.6𝑖𝑛3
𝑉 = 166.7𝜋
𝑉 =4𝜋(3)3
3
𝑉 = 113.1𝑐𝑚3
𝑉 = 36𝜋
𝑉 = 11494𝑖𝑛3 𝑉 = 7238.2𝑚3
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Composite Solid
Composite Solid = Volume 1 + Volume 2
𝑉 =1
2∙4𝜋(6)3
3
𝑉 = 1922.7𝑖𝑛3
𝑉 = 144𝜋 + 468𝜋
+ 𝜋 6 2(13)
𝑉 = 612𝜋
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
Composite Solid
Composite Solid = Volume 1 + Volume 2
𝑉 =(4)(4)(6)
3
𝑉 = 112𝑖𝑛3
𝑉 = 32 + 80
+ (4)(4)(5)
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
How will I show you that I’ve learned it?
Daily 5 Question Check for Understanding
Daily Ticket out the Door
What am I going to do today?
Volume of Sphere
Volume of Cones
Volume of Rectangular and Triangular Pyramid
What am I learning today?
G.GMD.1 Give informal arguments for
geometric formulas
G.GMD.3 Use volume formulas to solve
problems
How will I show you that I’ve learned it?
Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cross Sections3-Dimensional
Figures
What am I learning today?
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and rotations
polyhedron
edgeface vertex diagonal
Cross section
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Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cross Sections3-Dimensional
Figures
What am I learning today?
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and rotations
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Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cross Sections3-Dimensional
Figures
What am I learning today?
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and rotations
polygon
circles
congruent
similar
circle triangle square
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Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cross Sections3-Dimensional
Figures
What am I learning today?
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and rotations
rectangle triangle triangle
axis
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Daily 5 Question Check for
Understanding
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What am I going to do today?
Cross Sections3-Dimensional
Figures
What am I learning today?
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and rotations
How will I show you that I’ve learned it?
Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cross Sections3-Dimensional
Figures
What am I learning today?
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and rotations
How will I show you that I’ve learned it?
Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cross Sections3-Dimensional
Figures
What am I learning today?
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects and rotations
How will I show you that I’ve learned it?
Daily 5 Question Check for
Understanding
Daily Ticket out the Door
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Cavalieri’s Principle Density
What am I learning today?
G.GMD.2 Give an informal argument using Cavalieri’s Principle for the formulas for the
volume of a sphere and other solids
𝑽 = 𝝅𝒓𝟐𝒉
𝑉 = 𝜋(5)2(12)
𝑉 = 942.5𝑚3
𝑉 = 300𝜋
Cylinder A:
𝑉 = 𝜋(5)2(12)
𝑉 = 942.5𝑚3
𝑉 = 300𝜋
Cylinder B:
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Daily 5 Question Check for
Understanding
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What am I going to do today?
Cavalieri’s Principle Density
What am I learning today?
G.GMD.2 Give an informal argument using Cavalieri’s Principle for the formulas for the
volume of a sphere and other solids
How will I show you that I’ve learned it?
Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cavalieri’s Principle Density
What am I learning today?
G.GMD.2 Give an informal argument using Cavalieri’s Principle for the formulas for the
volume of a sphere and other solids
mass
sizedensity
mass volume
How will I show you that I’ve learned it?
Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cavalieri’s Principle Density
What am I learning today?
G.GMD.2 Give an informal argument using Cavalieri’s Principle for the formulas for the
volume of a sphere and other solids
𝑫 =𝑴
𝑽
𝑫 =𝑴
𝑽
Rock # 1 because the density is greater than rock #2
=45𝑔
15𝑐𝑚3= 3𝑔/𝑐𝑚3
=60𝑔
30𝑐𝑚3= 2𝑔/𝑐𝑚3
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Daily 5 Question Check for
Understanding
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What am I going to do today?
Cavalieri’s Principle Density
What am I learning today?
G.GMD.2 Give an informal argument using Cavalieri’s Principle for the formulas for the
volume of a sphere and other solids
𝑫 = 𝑴× 𝑽 =3.2𝑔
𝑚𝐿× 2𝑚𝐿 = 80𝑔
𝑫 =𝑴
𝑽=
500𝑔
240𝑐𝑚3= 21𝑔/𝑐𝑚3
How will I show you that I’ve learned it?
Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cavalieri’s Principle Density
What am I learning today?
G.GMD.2 Give an informal argument using Cavalieri’s Principle for the formulas for the
volume of a sphere and other solids
How will I show you that I’ve learned it?
Daily 5 Question Check for
Understanding
Daily Ticket out the Door
What am I going to do today?
Cavalieri’s Principle Density
What am I learning today?
G.GMD.2 Give an informal argument using Cavalieri’s Principle for the formulas for the
volume of a sphere and other solids
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