Transcript Document

How do you think through and answer a real
world problem involving cones?
For example:
A conical glass flower vase has a
base that is 6 inches in diameter
and the vase holds approximately
113 cubic inches of water. What is
the height of the vase?
In this lesson you will learn
how to solve real world
problems by finding the
volume of cones.
Let’s
Review
Let’s
Review
Volume of Cone
h
B= πr2
1
V = πr2h
3
Let’s
Review
Let’s
Review
250 cubic inches of
water means I have a
volume of 250 in3
in
length
in2
area
in3
volume
CoreReview
Lesson
Let’s
A conical glass flower vase has a
base that is 6 inches in diameter
and the vase holds approximately
113 cubic inches of water. What is
the height of the vase?
1
V = πr2h
3
CoreReview
Lesson
Let’s
1
V = πr2h
3
d=6 in
so r=3 in
Given: radius = 3 in
volume = 113 in3
Find: height = ???
CoreReview
Lesson
Let’s
1
V = πr2h
3
113
in3 =
1
π(3in)2 xh
3
113 in3 = 3πin2 xh
113 in3
h=
3π in2
height ≈ 12 in
A Common
Let’s
Review Mistake
1
V = πr2h
3
V = 25.13 in3
1
V = π(2in)2 x 25.13 in3
3
= 1.33πin2 x 25.13 in3
≈ 105 in5
r= 2in
Actual: h = 6 in
In this lesson you learned how
to solve real world problems
by finding the volume of
cones.
Guided
Practice
Let’s
Review
A wax candle is in the shape of a right
circular cone. The height of the candle
is 9cm and the candle contains
approximately 167.55 cm3 of wax.
What is the radius of the candle?
Guided
Practice
Let’s
Review
Find: radius= ??
Given: height = 9 cm
volume = 113.1 cm3
V=
1
πr2h
3
113.1 cm3 = π(r)2 x9cm
3
113.1
cm
r2 =
9π cm
r = 4 cm2
= 2 cm
Guided
Practice
Let’s
Review
A cement truck dumps 37.7 cubic feet of
cement mix at a construction site in the shape
of a conical mound. The base of the pile of
cement has an approximate diameter of 6 ft.
How tall is the mound of cement?
Guided
Practice
Let’s
Review
1
V = πr2h
3
Find: height = ??
Given: diameter = 6 ft
volume = 37.7 ft3
37.7
ft3 =
1
π(3ft)2 xh
3
37.7 ft3
h=
3π ft2
h = 4 ft
Extension
Let’s
ReviewActivities
An ice cream shop stores ice cream in
cylindrical containers that are 25 cm tall
with radius 15 cm. They sell scoops of ice
cream that are 6 cm in diameter.
Approximately how many scoops of ice
cream will the store be able to serve out of
one full cylindrical container?
Quick Quiz
Let’s
Review
1. An ice cream cone has a radius of 2 in.
How much melted ice cream will the cone
hold if it has a height of 6 inches?
2. An art sculpture has a base in the shape
of a cone. It took approximately 2.1 cubic
ft of cement to make the base which has a
diameter of 2 ft. How tall is the base?