Holt CA Course 1 10-8 Volume of Prisms MG1.3 Know and use the formulas for the volume of triangular...
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Transcript of Holt CA Course 1 10-8 Volume of Prisms MG1.3 Know and use the formulas for the volume of triangular...
Holt CA Course 1
10-8 Volume of Prisms
MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.Also covered: AF3.1, AF3.2
California Standards
Holt CA Course 1
10-8 Volume of Prisms
You need 10, or 5 · 2, centimeter cubes to cover the bottom of this rectangular prism.
You need 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes.
Holt CA Course 1
10-8 Volume of Prisms
Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cubic centimeters, or 30 cm3.
Holt CA Course 1
10-8 Volume of Prisms
The volume of a rectangular prism is the area of its base times its height. This formula can be used to find the volume of any prism.
Holt CA Course 1
10-8 Volume of PrismsTeacher Example 1: Finding the Volume of a
Rectangular Prism
Find the volume of the rectangular prism.
B = 26 · 11 The base is a rectangle.
Multiply.B = 286
13 in.
26 in.11 in.
Step 1: Find the area of the base.
Holt CA Course 1
10-8 Volume of PrismsTeacher Example 1 Continued:
Find the volume of the rectangular prism.
V = Bh Write the formula.
V = 286 • 13 Substitute for B and h.
Multiply.V = 3,718 in3
13 in.
26 in.11 in.
Step 2: Find the volume.
The volume of the prism is 3,718 in3.
Holt CA Course 1
10-8 Volume of Prisms
Student Practice 1: Find the volume of the rectangular prism.
B = 29 · 12 The base is a rectangle.
Multiply.B = 348
Step 1: Find the area of the base.
16 in.
29 in.12 in.
Holt CA Course 1
10-8 Volume of PrismsStudent Practice 1 Continued: Find
the volume of the rectangular prism.
V = Bh Write the formula.
V = 348 • 16 Substitute for B and h.
Multiply.V = 5,568 in3
Step 2: Find the volume.
The volume of the prism is 5,568 in3.
16 in.
29 in.12 in.
Holt CA Course 1
10-8 Volume of Prisms
You can also use the formula V= Bh to find the volume of a triangular prism. For triangular prisms, B represents the area of a triangle, rather than a rectangle.
Holt CA Course 1
10-8 Volume of PrismsTeacher Example 2: Finding the Volume of a
Triangular Prism
Find the volume of each triangular prism.
A. Step 1: Find the area of the base.
The base is a triangle.B = ( • 3.9 • 1.3) 12__
Multiply.B = 2.535
Holt CA Course 1
10-8 Volume of PrismsTeacher Example 2A: Finding the Volume of a
Triangular Prism Continued
Find the volume of each triangular prism.
A. Step 2: Find the volume.
V = Bh Write the formula.
V = 2.535 • 4 Substitute for B and h.
Multiply.V = 10.14 m3
The volume of the prism is 10.14 m3.
Holt CA Course 1
10-8 Volume of Prisms
The height of a prism is the distance between its two bases.
Caution!
Holt CA Course 1
10-8 Volume of PrismsTeacher Example 2B: Finding the Volume of a
Triangular Prism
Find the volume of each triangular prism.
B. Step 1: Find the area of the base.
The base is a triangle.B = ( • 6.5 • 7) 12__
Multiply.B = 22.75
Holt CA Course 1
10-8 Volume of PrismsTeacher Example 2B: Finding the Volume of a
Triangular Prism Continued
Find the volume of each triangular prism.
B. Step 2: Find the volume.
V = Bh Write the formula.
V = 22.75 • 6 Substitute for B and h.
Multiply.V = 136.5 ft3
The volume of the prism is 136.5 ft3.
Holt CA Course 1
10-8 Volume of PrismsStudent Practice 2A:
Find the volume of each triangular prism.
A. Step 1: Find the area of the base.
The base is a triangle.B = ( • 4.2 • 1.6) 12__
Multiply.B = 3.36
1.6 m 7 m
4.2 m
Holt CA Course 1
10-8 Volume of PrismsStudent Practice 2A Continued:
Find the volume of each triangular prism.
A. Step 2: Find the volume.
V = Bh Write the formula.
V = 3.36 • 7 Substitute for B and h.
Multiply.V = 23.52 m3
The volume of the prism is 23.52 m3.
1.6 m 7 m
4.2 m
Holt CA Course 1
10-8 Volume of PrismsStudent Practice 2B:
Find the volume of each triangular prism.
B. Step 1: Find the area of the base.
The base is a triangle.B = ( • 4.5 • 9) 12__
Multiply.B = 20.25
4.5 ft5 ft
9 ft
Holt CA Course 1
10-8 Volume of PrismsStudent Practice 2B Continued: Find
the volume of each triangular prism.
B. Step 2: Find the volume.
V = Bh Write the formula.
V = 20.25 • 5 Substitute for B and h.
Multiply.V = 101.25 ft3
The volume of the prism is 101.25 ft3.
4.5 ft5 ft
9 ft
Holt CA Course 1
10-8 Volume of Prisms
Teacher Example 3: Application
An artist wants to make glass paper-weights with the dimensions shown. He estimates that he will need less than 20 cubic centimeters of glass for each paperweight. Is his estimate reasonable? Explain.
Step 1: Find the area of the base.
The base is a triangle.B = • 6 • 5.2 = 15.612__
5.2 cm
6 cm
3 cm
Holt CA Course 1
10-8 Volume of PrismsTeacher Example 3 Continued
An artist wants to make glass paper-weights with the dimensions shown. He estimates that he will need less than 20 cubic centimeters of glass for each paperweight. Is his estimate reasonable? Explain.
Step 2: Find the volume.5.2 cm
6 cm
3 cm
V = Bh Write the formula.
V = 15.6 • 3 = 46.8 cm3 Substitute for B and h.
No; each paperweight will require about 47 cm3 of glass.
Holt CA Course 1
10-8 Volume of Prisms
Student Practice 3:
An architect wants to make a model building with the dimensions shown. He estimates that he will need more than 60 cubic centimeters of paper for each building. Is his estimate reasonable? Explain.
Step 1: Find the area of the base.
The base is a triangle.B = • 6 • 5.5 = 16.512__
5.5 cm
6 cm
5 cm
Holt CA Course 1
10-8 Volume of Prisms
Step 2: Find the volume.
V = Bh Write the formula.
V = 16.5 • 5 = 82.5 cm3 Substitute for B and h.
No; each building will require about 83 cm3 of paper.
5.5 cm
6 cm
5 cm
Student Practice 3 Continued:
An architect wants to make a model building with the dimensions shown. He estimates that he will need more than 60 cubic centimeters of paper for each building. Is his estimate reasonable? Explain.