Transcript Volumes of Pyramids and Cones LESSON 11-5 Additional Examples Find the volume of a square pyramid with base edges 15 cm and height 22

Volumes of Pyramids and Cones
LESSON 11-5
Additional Examples
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.
1
V = 3 Bh
1
Use the formula for volume of a pyramid.
= 3 (225)(22)
Substitute 225 for B and 22 for h.
= 1650
Simplify.
The volume of the square pyramid is 1650 cm3.
Quick Check
HELP
GEOMETRY
Volumes of Pyramids and Cones
LESSON 11-5
Additional Examples
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.
HELP
GEOMETRY
Volumes of Pyramids and Cones
LESSON 11-5
Additional Examples
(continued)
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.
Step 1: Find the height of the pyramid.
172 = 82  h2
Use the Pythagorean Theorem.
289 = 64  h2
Simplify.
225 = h2
Subtract 64 from each side.
h = 15
HELP
Find the square root of each side.
GEOMETRY
Volumes of Pyramids and Cones
LESSON 11-5
Additional Examples
(continued)
Step 2: Find the volume of the pyramid.
1
Use the formula for the volume of a pyramid.
= 3 (16  16)15
1
Substitute.
= 1280
Simplify.
V = 3 Bh
The volume of the square pyramid is 1280 m3.
Quick Check
HELP
GEOMETRY
Volumes of Pyramids and Cones
LESSON 11-5
Additional Examples
Find the volume of the cone below in terms of
.
1
r = 2 d = 3 in.
1
r 2h
Use the formula for volume of a cone.
1
(32)(11)
Substitute 3 for r and 11 for h.
V= 3
=3
= 33
Simplify.
The volume of the cone is 33
HELP
in.3.
Quick Check
GEOMETRY
Volumes of Pyramids and Cones
LESSON 11-5
Additional Examples
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.
d
r = 2 =2
1
r 2h
Use the formula for the volume of a cone.
1
(22)(7)
Substitute 2 for r and 7 for h.
V= 3
V= 3
Use a calculator.
About 29 cm3 of ice cream can fit entirely inside the cone.
HELP
Quick Check
GEOMETRY