Pre Algebra
Section 6.3
Unit 6 – Coordinate Plane and Geometry
Section 3 –Volume
Volume
When we find the Volume of a shape, we are finding the number of 1 unit X 1 unit X 1 units boxes fit in
the shape.
Volume of a Rectangular Prism
ܸ‫ݐ ݂݋ ܽ݁ݎܣ( = ݁݉ݑ݈݋‬ℎ݁ ‫݃݁݅ܪ ∙ )݁ݏܽܤ‬ℎ‫ݐ‬
H
ܸ =‫ܪ∙ܤ‬
ܸ = (ܾ ∙ ℎ) ∙ ‫ܪ‬
‫ݓ‬
݈
ܸ =݈∙‫ܪ∙ݓ‬
Example 1)
Find the Volume of the rectangular prism below.
2cm
4cm
10cm
ܸ =݈∙‫ܪ∙ݓ‬
ܸ = 10ܿ݉ ∙ 4ܿ݉ ∙ 2ܿ݉
ܸ = 80
The Volume is 80ܿ݉ ଷ .
Notice the units are to the 3rd power – we increase a power for each dimension.
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Pre Algebra
Section 6.3
Volume of a cylinder
‫ݎ‬
ܸ‫ݐ ݂݋ ܽ݁ݎܣ( = ݁݉ݑ݈݋‬ℎ݁ ‫݃݅݁ܪ ∙ )݁ݏܽܤ‬ℎ‫ݐ‬
‫ܪ‬
ܸ =‫ܪ∙ܤ‬
ܸ = (ߨ‫ ݎ‬ଶ ) ∙ ‫ܪ‬
Example 2) Find the volume of the cylinder below.
2m
ܸ = (ߨ‫ ݎ‬ଶ ) ∙ ‫ܪ‬
7m
ܸ = (3.14 ∙ 2ଶ ) ∙ 7
ܸ = 3.14 ∙ 4 ∙ 7
ܸ = 12.56 ∙ 7
ܸ = 87.92
The Volume is 87.92݉ ଷ.
Volume of a Pyramid
ଵ
ܸ‫ = ݁݉ݑ݈݋‬ଷ (‫ݐ ݂݋ ܽ݁ݎܣ‬ℎ݁ ‫݃݁݅ܪ ∙ )݁ݏܽܤ‬ℎ‫ݐ‬
ଵ
‫ܪ‬
ܸ = ଷ‫ܪ∙ ܤ‬
ଵ
ܸ = ଷ (ܾ ∙ ℎ ) ∙ ‫ܪ‬
ଵ
ܸ = ଷ݈ ∙‫ܪ ∙ ݓ‬
‫ݓ‬
݈
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Pre Algebra
Section 6.3
Example 3) Find the Volume of the Pyramid below.
ଵ
ܸ = ଷ݈ ∙‫ܪ ∙ ݓ‬
10݅݊
ଵ
ܸ = ଷ ∙ 4 ∙ 6 ∙ 10
ܸ = 80
The Volume is 80݅݊ଷ
4݅݊
6݅݊
Volume of a Cone
ଵ
ܸ‫ = ݁݉ݑ݈݋‬ଷ (‫ݐ ݂݋ ܽ݁ݎܣ‬ℎ݁ ‫݃݁݅ܪ ∙ )݁ݏܽܤ‬ℎ‫ݐ‬
ଵ
ܸ = ଷ‫ܪ∙ ܤ‬
ଵ
ܸ = ଷ (ߨ‫ ݎ‬ଶ ) ∙ ‫ܪ‬
Example 4) Find the Volume of the cone below.
ଵ
ܸ = ଷ (ߨ‫ ݎ‬ଶ ) ∙ ‫ܪ‬
7݉
ଵ
3݉
ܸ ≈ ଷ (3.14 ∙ 3ଶ ) ∙ 7
ଵ
ଵ
ܸ ≈ ଷ ∙ 3.14 ∙ 9 ∙ 7
Multiplying ଷ ∙ 9 eliminates
the fraction.
ܸ ≈ 65.94
The Volume is approximately 65.94݉ ଷ
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Pre Algebra
Section 6.3
Volume of a Sphere
ܸ‫= ݁݉ݑ݈݋‬
‫ݎ‬
ସ
ଷ
ߨ‫ ݎ‬ଷ
Example 5) Find the Volume of the sphere below.
ܸ=
3݂‫ݐ‬
ܸ≈
ܸ≈
ସ
ଷ
ସ
ଷ
ସ
ଷ
ߨ‫ ݎ‬ଷ
∙ 3.14 ∙ 3ଷ
∙ 3.14 ∙ 27
ܸ ≈ 113.04
The Volume of the sphere is 113.04݂‫ ݐ‬ଷ
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Pre Algebra
Section 6.3
Exercise 6.3
NAME:___________________________________
Calculate the volume of each of the following.
For problems 1-3 consider the rectangular prism below.
1. ݈ = 2݂‫ݐ‬, ‫ = ݓ‬3݂‫ݐ‬, ‫ = ܪ‬4݂‫ݐ‬
‫ܪ‬
݈
‫ݓ‬
ଶ
ଵ
2. ݈ = ଷ ݉, ‫ = ݓ‬5݉, ‫ = ܪ‬ଶ ݉
3. ݈ = 2.5݅݊, ‫ = ݓ‬1.2݅݊, ‫ = ܪ‬4݅݊
For problems 4-6 consider the cylinder below.
‫ݎ‬
4. ‫ = ݎ‬2.1ܿ݉, ‫ = ܪ‬3ܿ݉
‫ܪ‬
ଵ
6. ‫ = ݎ‬ଷ ݂‫ݐ‬, ‫ = ܪ‬5݂‫ݐ‬
5. ‫ = ݎ‬5݅݊, ‫ = ܪ‬4݅݊
For Problems 7-9 consider the Rectangular pyramid below
ଵ
‫ܪ‬
7. ݈ = ଶ ܿ݉, ‫ = ݓ‬3ܿ݉, ‫ = ܪ‬4ܿ݉
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݈
‫ݓ‬
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Pre Algebra
8. ݈ = 2.1݉, ‫ = ݓ‬3݉, ‫ = ܪ‬4݉
Section 6.3
9. ݈ = 5݂‫ݐ‬, ‫ = ݓ‬2݂‫ݐ‬, ‫ = ܪ‬6݂‫ݐ‬
For Problems 10-12 consider the cone below
10. ‫ = ݎ‬2.5ܿ݉, ‫ = ܪ‬4ܿ݉
‫ܪ‬
‫ݎ‬
ଵ
11. ‫ = ݎ‬ହ ݂‫ݐ‬, ‫ = ܪ‬4݂‫ݐ‬
12. ‫ = ݎ‬6݉, ‫ = ܪ‬2݉
For Problems 13-15 consider the sphere below
13. ‫ = ݎ‬5݉
‫ݎ‬
ଵ
14. ‫ = ݎ‬ଶ ܿ݉
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15. ‫ = ݎ‬2.2݂‫ݐ‬
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