Chapter 14 Lesson 3
Solids with Circles
Parts of a Cone
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I'm getting tired of doing
areas of shapes I don't like.
I didn't know this was
a popularity contest.
Besides, you liked doing triangle prism.
You mean tent. Yeah, I
like to camp, so it was cool.
Ok, I have a
solid I think you'll like.
You eat alot of these things.
Eat alot of them?
I don't know what that is.
Oh, and this is
one of your favorite foods.
I eat road markers?
That's 1 way they're used.
Here's another way.
Turn it over. Put a circle on top.
Oh, ice cream cone.
I'll show you how I eat them.
Of course, the more the better.
So, what are we doing now?
Surface Area
Oh, figures. Surface area.
How many faces are there?
circle
triangle
A circle and a long triangle.
That's pretty much it.
circle
triangle
How many vertices are there?
#1
1 Vertice
Exactly 1 vertice.
That's not very much.
Yeah, but why is it different
from the other solids we did?
Well, it's sharp
like all the other points.
How many faces are there?
Ohhh, just 1 face wraps
around instead of 4 faces.
Yup. How many edges are there?
1 Edge
#1
Same thing, 1 edge.
Is that enough?
1 Edge
#1
Well, we're running out of time.
We'll do the rest tomorrow.
Qs
How many faces are in a cone?
2 faces
Cone has a circle base
and triangle side.
How many edges and
vertices are in a cone?
1 edge
1 vertice
The edge is the base of the circle.
Chapter 14 Lesson 3a
Solids with Circles
Surface Area of Cone
Cone Parts
Well, we did the cone parts. Now
it's time for the... that is so funny.
Mr G? You okay?
You never laugh in math.
Sorry, when I was a kid, there
was a TV skit call cone heads.
It was so funny
and this reminds me of it.
Kind of like when you thought
the circle looked like Pac Man?
No problem. Take your time.
It wasn't that funny.
Ok, I'll get a radius for it.
2 ft
I already know the answer.
2 ft
Good thing. We've
done it enough times.
2
3.1 x 2
3.1 x 4 = 12.4 sq ft
Ok, now the triangle.
I'll need another measurement.
2 feet
The side of the cone is 2 feet tall.
2 feet
I'll show you the other way.
? feet
.............
2 ft
2 ft
Yeah, that looks alot better.
? feet
.............
2 ft
2 ft
Here's the tricky part.
How long is the triangle?
Pi x Diameter
3.1 x 4 = 12.4
2 ft
12.4 ft
Use the diameter is 12.4 ft.
Same as the other.
Pi x Diameter
3.1 x 4 = 12.4
2 ft
12.4 ft
What's the triangle area?
12.4 feet
2 ft
...............
12.4 x 2
Multiply base x height.
12.4 feet
2 ft
...............
12.4 x 2
Don't forget to divide by 2.
12.4 feet
...............
12.4 sq ft
2 ft
So, they cancel out.
12.4 feet
...............
12.4 sq ft
2 ft
Ok, finish the adding thing.
12.4
+ 12.4
12.4 sq ft
12.4 sq ft
Area of the circle + the triangle.
12.4
+ 12.4
12.4 sq ft
12.4 sq ft
What's the surface area?
12.4
+ 12.4
24.8 sq ft
It's 24.8 square feet.
Too easy for rock n roll.
I wish rock n roll was that easy.
What did it do for surface area?
1. Area of circle base.
2. Diameter of the base.
3. Multiply with the side.
You know, I'm not surprised.
Oooh, there's 1 more thing.
.............
2 feet
What if we told you the height
instead of the outside cone?
.............
2 feet
Where do you get this from?
.............
2 feet
It can happen. The question
is, what formula do you use?
.............
2 feet
Well, looks like a triangle to me.
2
2
a +b =c
That would be the
Pythagorean Theorem.
2
2
2
a +b =c
See? I knew
what I was talking about.
2
So, you really, really have to
check if it's height or side it uses.
Trust me. Side is alot easier.
Qs
1. Area of circle base.
2. Diameter of ?
3. ?
Name 3 steps to find surface area
of a cone when you know the side.
1. Area of circle base.
2. Diameter of the base.
3. Multiply with the side.
Add the circle and triangle.
What formula finds the outside if
you know the height of the cone?
2
2
a +b =c
2
Pythagorean Theorem
finds the side of the cone.
Chapter 14 Lesson 3
Solids with Circles
Parts and surface
area of a Cone
Cone
We use cones alot. From ice cream
to road markers, they are common.
How many faces are there?
circle
triangle
2 Faces
A circle and a long triangle.
How many vertices are there?
#1
1 Vertice
Exactly 1 vertice.
How many edges are there?
1 Edge
#1
Same thing, 1 edge.
We'll put a radius in for the circle.
1 ft
You probably know the answer.
What's the area of the circle?
2
3.1 x 1
3.1 x 1 = 3.1 sq ft
It's 3.1 square feet.
What else do we need?
2 feet
The side of the cone is 2 feet tall.
We'll show you the other way.
? feet
.............
2 ft
1 ft
Find the triangle's length.
How do you do that?
? feet
.............
2 ft
1 ft
Use the diameter of the circle.
What is this diameter?
Pi x Diameter
3.1 x 2 = 6.2
2 ft
6.2 ft
Multiply 3.1 x 2.
Diameter is 6.2 feet long.
What's the triangle area?
6.2 feet
2 ft
...............
6.2 x 2
Multiply base x height.
What will add together?
12.4
+ 6.2
12.4 sq ft
6.2 sq ft
Area of circle + triangle.
What's the surface area?
12.4
+ 6.2
18.6
sq ft
The cone's surface area
is 18.6 square feet.
Questions
Name 3 steps to find
surface area of a cone when
you know the side of it.
1. Area of circle base.
2. Diameter of the base.
3. Multiply with the side.
Add the circle and triangle.
How does it change with the height
of the cone instead of the side?
2
2
a +b =c
2
Use the Pythagorean Theorem
to find the side of the cone.
Chapter 14 Lesson 3
Solids with Circles
Practice #1
Parts and surface
area of a Cone
How many edges and
vertices does a cone have?
1 vertice
1 edge
The edge is a circle at the bottom.
How many
faces does a cone have?
The base is a circle
and the cone is a triangle.
1. Area of circle base.
2. Diameter of ?
3. ?
Name 3 steps to find surface area
of a cone when you know the side.
1. Area of circle base.
2. Diameter of the base.
3. Multiply with the side.
Add the circle and triangle.
What formula finds the outside if
you know the height of the cone?
2
2
a +b =c
2
Pythagorean Theorem
finds the side of the cone.
Problems
3 ft
2 ft
What are the 2 parts to
a cone surface area?
2 ft
3 ft
Add the area of the base (circle)
and the cone (triangle).
What is area of the circle?
2
3.1 (2) = 12.4
Pi R squared
The circle is 12.4 sq feet.
sq ft
2 ft
3 ft
What do you need to find
the area of a triangle?
2 ft
3 ft
Find the Perimeter
of the Circle
What do you use to find it?
4 ft
3 ft
Change radius to diameter.
Diameter is 4 feet.
What is the perimeter?
4 ft
12.4 ft
3 ft
12.4 ft
Multiply Pi x 4 = 12.4 ft
What's the area of the triangle?
3 ft
12.4 ft
Multiply and divide by 2.
37.4 2 = 18.7
sq ft
How do you find the surface area?
Circle: = 12.4 sq ft
Triangle: = 18.7 sq ft
How do you
get the total surface area?
Circle: = 12.4 sq ft
Triangle: = 18.7 sq ft
31.1 sq ft
Add them to get 31.1 sq feet.
Chapter 14 Lesson 3
Solids with Circles
Practice #2
Parts and surface
area of a Cone
How many edges and
vertices does a cone have?
1 vertice
1 edge
The edge is a circle at the bottom.
................
How do you use if you
know the height of the cone?
................
Pythagorean
Theorem
Use Pythagorean Theorem
to find the outside distance.
1. Area of circle base.
2. Diameter of ?
3. ?
Name 3 steps to find surface area
of a cone when you know the side.
1. Area of circle base.
2. Diameter of the base.
3. Multiply with the side.
Add the circle and triangle.
What formula finds the outside if
you know the height of the cone?
2
2
a +b =c
2
Pythagorean Theorem
finds the side of the cone.
3 ft
................
Problems
2 ft
What is the
Pythagorean Theorem?
................
3 ft
2
2 ft
2
a +b =c
2
A squared + B squared = C squared
Which numbers go where?
2
................
3 ft
2 ft
2
3 +2 =c
2
Put 3 in for A and 2 in for B.
Solve the next 2 steps.
2
2
2
3 +2 =c
2
13 = c
What happens next?
2
2
2
3 +2 =c
2
13 = c
13 = c
Take the square root.
What's the square root of 13?
2
2
2
3 +2 =c
2
13 = c
13 = c
3.6 = c
13 is between 9 and 16.
C is 3.6. What did you find?
................
3 ft
3.6 ft
2 ft
c is 3.6 ft
That's the side of the cone.
Chapter 14 Lesson 3
Solids with Circles
Performance #1
Parts and surface
area of a Cone
5 ft
2 ft
A cone is a circle and triangle.
What is the area of the circle?
5 ft
2 ft
12.4
sq ft
3.1 x 2
2
is 3.1 x 4
12.4 sq ft
Area is Pi R squared.
2 ft
5 ft
What do you need to find
the area of the triangle?
2 ft
5 ft
The Diameter
The diameter of the circle
makes the base of the triangle.
12.4
2 ft
5 ft
12.4 ft
Multiply Pi x 4 = 12.4 ft
What is the area of the triangle?
5 ft
12.4 ft
62
2
31 sq ft
Multiply and divide by 2.
12.4
sq ft
31 sq ft
12.4
31
circle
triangle
How do you find the surface area?
Circle: = 12.4 sq ft
Triangle: = 31 sq ft
43.4 sq ft
Add them to get 43.4 sq ft.
................
4 ft
2 ft
If you know the inside height,
what formula finds the side?
................
4 ft
2
2 ft
2
a +b =c
2
A squared + B squared = C squared
Which numbers go where?
2
................
4 ft
2 ft
2
4 +2 =c
2
Put 4 in for A and 2 in for B.
Solve the next 2 steps.
2
2
2
4 +2 =c
2
20 = c
What happens next?
2
2
2
4 +2 =c
2
20 = c
20 = c
Take the square root.
What's the square root of 20?
2
2
2
4 +2 =c
2
20 = c
20 = c
Take the square root.
What's the square root of 20?
2
2
2
4 +2 =c
2
20 = c
20 = c
4.5 = c
20 is between 16 and 25.
C is 4.5. What did you find?
................
4 ft
4.5 ft
2 ft
c is 4.5 ft
The side of the cone is 4.5 ft.
Chapter 14 Lesson 3
Solids with Circles
Performance #2
Parts and surface
area of a Cone
2 ft
2 ft
A cone is a circle and triangle.
What is the area of the circle?
2 ft
2 ft
12.4
sq ft
3.1 x 2
2
is 3.1 x 4
12.4 sq ft
Area is Pi R squared.
2 ft
2 ft
What do you need to find
the area of the triangle?
2 ft
2 ft
The Diameter
The diameter of the circle
makes the base of the triangle.
12.4
2 ft
2 ft
12.4 ft
Multiply Pi x 4 = 12.4 ft
What is the area of the triangle?
2 ft
12.4 ft
24.8
2
12.4 sq ft
Multiply and divide by 2.
12.4
sq ft
12.4 sq ft
12.4
12.4
circle
triangle
How do you find the surface area?
Circle: = 12.4 sq ft
Triangle: = 12.4 sq ft
24.8 sq ft
Add them to get 24.8 sq ft.
................
5 ft
2 ft
If you know the inside height,
what formula finds the side?
................
5 ft
2
2 ft
2
a +b =c
2
A squared + B squared = C squared
Which numbers go where?
2
................
5 ft
2 ft
2
5 +2 =c
2
Put 5 in for A and 2 in for B.
Solve the next 2 steps.
2
2
2
5 +2 =c
2
29 = c
What happens next?
2
2
2
5 +2 =c
2
29 = c
29 = c
Take the square root.
What's the square root of 29?
2
2
2
5 +2 =c
2
29 = c
29 = c
5.4 = c
29 is between 25 and 36.
C is 5.4. What did you find?
................
5 ft
5.4 ft
2 ft
c is 5.4 ft
The side of the cone is 5.4 ft.