This document provides instruction on calculating the volumes of cylinders, cones, and spheres. It defines key terms like radius, height, volume, and presents the formulas. For cylinders, the volume formula is given as V = πr^2h. For cones, the formula is the same as cylinders but divided by 1/3. For spheres, the volume formula is V = 4/3πr^3. Examples are shown for each shape calculating volumes when given the radius and height. In the summaries, the learner reflects on what they've learned about each shape's volume formula and if they can answer the lesson's essential question.

1. GEOMETRY
Volume of Cylinders,
Cones, Spheres
8th Math
Presented by Mr. Laws

2. Standard
8.G.9 – Know the formulas for the volumes of
cones, cylinders, and spheres and use them to
solve real-world and mathematical problems.

3. Essential Question
Using math principles, what is the effect
on the volume of a cylinder, cones, or
sphere once the radius or height has
change?

4. Target Statement
 I CAN find the volume of a cylinder.
 I CAN find the volume of a cone.
 I CAN find the volume of a sphere.

5. Definitions
• 3 Dimensional (3-D) – It is the length, width, and
height of solid figures.
• Prisms – are 3-D figures that have two bases.
Example: Cylinder.
• Pyramids 3-D figures that have one base.
Example: Cones
• Sphere a 3-D figure that is shape like a ball or
globe.
• Hemi-sphere – is half of a sphere or round solid
figure.

6. Volume of Solid Figures
Volume is the amount of
cubic units that can fit or
into or fill a solid figure.
All volume answers will be in Cubic Units!
Example: 25 ft3, 2560 m3, etc…

7. Solid Figures
Prisms have two bases such as a cylinder, cube, rectangular, and triangular
prisms.
Pyramids have one base, such as a square pyramid, triangular pyramid, and
cone.

8. Part I : Finding the Volume of a Cylinder
Radius (r)
Height (h)
𝑉 = 𝜋𝑟2ℎ
𝝅 = 𝒑𝒊 𝒐𝒓 𝟑. 𝟏𝟒
r2 = radius x radius
V = volume
h = height
Formula:

9. Finding the Volume of a Cylinder?
5 m
10 m
𝑉 = 𝜋𝑟2ℎ
𝑽 = 𝝅52 x 10
V = 785 m3
Use 3.14 for pi
𝑽 = 𝟑. 𝟏𝟒 𝒙 52 x 10
Note: If you use calculator pi, it will give you a more accurate decimal answer.
Example # 1

10. Finding the Volume of a Cylinder?
7 yds
12 yds
𝑉 = 𝜋𝑟2ℎ
𝑽 = 𝝅3.52 x 12
V = 461.6 yd3
Use 3.14 for pi
𝑽 = 𝟑. 𝟏𝟒 𝒙 3.52 x 12
What do you notice about this
problem?
Example # 2

11. Part I
SUMMARY
• What are some key concepts you should remember
about finding the volume of a cylinder
• Is there more you need to learn about this concept?
• Can you answer the essential question or do you have any
more questions concerning this lesson?

12. Part II: Finding the Volume of a Cone
Finding the volume of a cone uses
the same formula as finding the
volume of cylinder except it is
divided by 1/3 (one-third).

13. Finding the Volume of a Cone
𝑽 =
𝝅82 x 15
𝟑
𝑽 =
𝟑𝟎𝟏𝟒. 𝟒
𝟑
V = 1004.8 m3
Use 3.14 for pi
Example # 3

14. Finding the Volume of a Cone
𝑽 =
𝝅22 x 𝟖. 𝟔
𝟑
𝑽 =
𝟏𝟎𝟖. 𝟎𝟐
𝟑
V = 36.006 in3
4 in.
8.6 in
Example # 4
Use 3.14 for pi

15. Part II
SUMMARY
• What are some key concepts you should remember
about finding the volume of a cone.
• Is there more you need to learn about this concept?
• Can you answer the essential question or do you have any
more questions concerning this lesson?

16. Part III: Finding the Volume of a Sphere
Finding the volume of a sphere is
equal to 4 times pi times radius
cube, divided by three.

17. Finding the Volume of a Sphere
𝑽 =
𝟒𝝅103
𝟑
𝑽 =
𝟏𝟐𝟓𝟔𝟎
𝟑
V = 4186.6 cm3
Use 3.14 for pi
Example # 5

18. Finding the Volume of a Sphere
𝑽 =
𝟒𝝅143
𝟑
𝑽 =
𝟑𝟒𝟒𝟔𝟒. 𝟔𝟒
𝟑
V = 11488.2 m3
Use 3.14 for pi
Example # 6

19. Part III
SUMMARY
• What are some key concepts you should remember
about finding the volume of a Sphere.
• Is there more you need to learn about this concept?
• Can you answer the essential question or do you have any
more questions concerning this lesson?