Transcript Surface Area of Prisms and Cylinders

Volume of Cones and
Pyramids
Geometry
Unit 5, Lesson 8
Mrs. King
Reminder: What is a Pyramid?

Definition:
A shape formed by
connecting triangles
to a polygon.
 Examples:
Reminder: What is a Cone?

Definition:
A shape formed from a
circle and a vertex
point.
 Examples:
s
Volume Of A Cone.
Consider the cylinder and cone shown below:
D
H
D
The diameter (D) of the
top of the cone and the
cylinder are equal.
H
The height (H) of the
cone and the cylinder are
equal.
If you filled the cone with water and emptied it into the
cylinder, how many times would you have to fill the cone to
completely fill the cylinder to the top ? 3 times.
This shows that the cylinder has three times the
volume of a cone with the same height and radius.
www.ltscotland.org.uk/Images/volumesofsolids_tcm4-123355.ppt
Formulas

Volume of a Cylinder:  Volume of a Cone:
V = pr2 h
2
V= 1/3 pr h
Example #1

Calculate the
volume of:
V= 1/3 pr2h
V= 1/3 (p)(7)2(9)
V = 147pm3
Example #2

Calculate the
volume of:
V= 1/3 pr2h
V= 1/3 (p)(5)2(12)
V = 100pcm3
Example #3:
An ice cream cone is 7 cm tall and 4 cm in diameter.
About how much ice cream can fit entirely inside the
cone? Find the volume to the nearest whole number.
r = d =2
2
V = 1 πr 2h
3
1
V = π(22)(7)
3
V ≈ 29.321531
About 29 cm3 of ice cream can fit entirely inside
the cone.
Compare

Compare a Prism to a Pyramid.

Make a conjecture to what the formula
might be for Volume of a Pyramid.
Formulas

Volume of a Prism:
V  Bh
B  base area

Volume of a Pyramid:
V = 1/3 Bh
Example #4

Calculate the
volume of:
15”
V = 1/3 Bh
V = 1/3 (102)(15)
V = 500in3
10”
Example #5
Find the volume of a square pyramid with base
edges 15 cm and height 22 cm.
Because the base is a square, B = 15 • 15 = 225.
V = 1 Bh
3
= 1 (225)(22)
3
= 1650
Example #6
Find the volume of a square pyramid with base edges 16 m
and slant height 17 m.
The altitude of a right square pyramid intersects the
base at the center of the square.
Because each side of the square base is 16 m, the
leg of the right triangle along the base is 8 m, as
shown below.
Example #6, continued
Step 1: Find the height of the pyramid.
172 = 82 + h2 Use the Pythagorean Theorem.
289 = 64 + h2
225 = h2
h = 15
Step 2: Find the volume of the pyramid.
V = 13 Bh
= 13 (16 x 16)15
= 1280