Math 8
Date:
LESSON PLAN #65
Topic: Geometry
Main Idea: Finding the Volume of Cones
Aim: How do we find the volume of cones?
H.W. #65: Ditto
DO-NOW #65: Answer the following questions. Show work.
1) Find the volume of the cylinder located at the left.
2) Three times as many robins as cardinals visited a bird feeder. If a total of 20 robins
and cardinals visited the feeder, how many were robins?
Let c = the number of cardinals and 3c = the number of robins
c + 3c = 4c = 20: c = 5 = the number of cardinals and 3(5) = 15 = the number of
robins
3) Find the percent of change if last month’s electric bill was $50.00 and this month’s bill is $57.20.
amount of increase/original amount = ($57.20 - $50.00)/$50.00 = $7.20/$50.00 = 14.4%
Go-Over: 1) H.W. #64 – Ditto
2) DO-NOW #65
Materials: Sage Kit (cylinder and cone which both will have the same circular base and same height), water,
food coloring
Motivation:
Show students the cylinder and cone. Ask them to compare both figures and list their comparisons on the board.
Hopefully students will notice that the only difference that the cylinder and cone will have is that the cylinder has 2 circular bases and
the cone has one with the other end being pointed.
The students should also realize that the base of the cone and the base of the cylinder are the same size.
The students should also realize that the height of the cone and height of the cylinder are the same.
Development and Methods:
Question: If you know how to find the height of a cylinder and you know the radius or diameter of its circular base, how
do you find the volume of a cylinder? What does volume mean?
Answer: Volume is the number of cubic units to fill a space.
Volume of a cylinder is πr2h.
Question: If you know how to find the volume of a cylinder, then how would you find the volume of a cone?
(Before they answer that question, ask students what today’s aim might be?)
Answer: (Have students help you with sage kit demo.)
Students will hopefully realize they will need to fill the cylinder with water completely
with three water filled cones.
Answer: If the volume of a cylinder is πr2h = (Area of base) x (Height of prism) and volume means the number of cubic
units to fill a space, then you would need to pour 3 water filled cones into the cylinder to completely fill it with water
without spilling over.
Question: With the previous conclusion that you came up with, now tell me as to how I could find the formula for the
volume of a cone
Answer: Since the volume of a cylinder is πr2h = (Area of base) x (Height of prism) and it takes 3 water filled cones
to fill the cylinder, then just take ⅓ of B x Height of cone to find the volume of the cylinder.
Volume of the pyramid is ⅓ x Area of Base x Height of cone
Math 8 – Lesson Plan #65 – Page 2
Drill: Answer the following questions. Show work.
Find the volume of:
1)
V = ⅓ x (3.14 x 3 x 3) x 6 = 3.14 x 3 x 6 = 3.14 x 18 = 56.52 ft2
2) What is the volume of a cone with a
radius of 6 ft and a height of 6 ft?
V = ⅓ x (3.14 x 6 x 6) x 6 = 3.14 x 2 x 6 x 6 = 3.14
x 72 = 226.08 ft2
6’
3’
3’
3) What would happen to the volume of a cone if the radius was doubled and the height remained the same?
Answer: The volume increases by 4x the smaller volume.
Summary: Volume of a cone =
where B = the area of the circular base and H = the height of the cone.
If time: Find the volume of the following cones:
1) Radius of the base = 4.5 cm and height = 15 cm
2) Diameter of the base = 12 mm and height = 9.3 mm
3) Tom’s closet is 1 m wide, 2 m high, and 1.5 m deep. What is the volume of his closet?
Sewanhaka High School
Math 8
Per:______________
Name:___________________________________
Mrs. Lidowsky, Principal
Mr. Long, Teacher
Date:________________________
H.W. #65: Ditto
DO-NOW #65: Answer the following questions. Show work.
1) Find
2) Three times as many robins as
the
cardinals visited a bird feeder. If a
volume of total of 20 robins and cardinals
the
visited the feeder, how many were
cylinder
robins?
located at
the left.
Topic: Geometry
Main Idea: Finding the volume of cones.
Aim:
RECALL
Lists some comparisons of the cone and cylinder.
If you know how to find the volume of a cylinder, then how
would you find the volume of a cone?
With the previous conclusion that you came up with, now tell
me as to how I could find the formula for the volume of a
cone.
NOTES
3) Find the percent of change if last
month’s electric bill was $50.00
and this month’s bill is $57.20.
Drill: Answer the following questions. Show work.
1) Find the volume of the cone below:
2) What is the volume of a cone with a
radius of 6 ft and a height of 6 ft?
6’
3’
3’
3) What would happen to the volume of a cone if the radius was doubled and the height remained the same?
Summary:
If time: Find the volume of the following cones:
1) Radius of the base = 4.5 cm and height = 15 cm
2) Diameter of the base = 12 mm and height = 9.3 mm
3) Tom’s closet is 1 m wide, 2 m high, and 1.5 m deep. What is the volume of his closet?
Sewanhaka High School
Mrs. Lidowsky, Principal
Math 8
Mr. Long, Teacher
Period:______________
Date:________________________
Name:___________________________________ (Use the back as more room to show your work.)
H.W. #65: Finding the Volume of Cones – Ans Key
Directions: Answer the following questions. Show your work.
3) Find the volume of the solid below:
4) Isaiah is making cone-shaped ice cubes by using a
mold. The radius of the mold is 1.5 inches and the
height is 2 inches. If one cubic inch is about 0.55
ounce, how many ounces will ten ice cubes weight?
Round to the nearest tenth. 25.9 oz
1/3(ᴫ(1.5)2)(2) is about 4.7 cubic inches volume for
each cube.
.55 oz(4.7 in3) is about 2.59 oz per cube.
10 cubes: 10(2.59) = 25.9 oz
5)
Sewanhaka High School
Mrs. Lidowsky, Principal
Math 8
Mr. Long, Teacher
Period:______________
Date:________________________
Name:___________________________________ (Use the back as more room to show your work.)
H.W. #65: Finding the Volume of Cones
Directions: Answer the following questions. Show your work.
3) Find the volume of the solid below:
5)
4) Isaiah is making cone-shaped ice cubes by using a
mold. The radius of the mold is 1.5 inches and the
height is 2 inches. If one cubic inch is about 0.55
ounce, how many ounces will ten ice cubes weight?
Round to the nearest tenth.