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GEOMETRYHELP
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 = Bh Use the formula for volume of a pyramid.13
= (225)(22) Substitute 225 for B and 22 for h.13
= 1650 Simplify.
The volume of the square pyramid is 1650 cm3.
Quick Check
Volumes of Pyramids and ConesLESSON 11-5
Additional Examples
GEOMETRYHELP
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.
Volumes of Pyramids and ConesLESSON 11-5
Additional Examples
GEOMETRYHELP
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 Find the square root of each side.
(continued)
Volumes of Pyramids and ConesLESSON 11-5
Additional Examples
GEOMETRYHELP
Step 2: Find the volume of the pyramid.
= 1280 Simplify.
The volume of the square pyramid is 1280 m3.
V = Bh Use the formula for the volume of a pyramid.13
= (16 16)15 Substitute.13
(continued)
Volumes of Pyramids and ConesLESSON 11-5
Additional Examples
Quick Check
GEOMETRYHELP
Find the volume of the cone below in terms of .
r = d = 3 in.12
V = r 2h Use the formula for volume of a cone.13
= (32)(11) Substitute 3 for r and 11 for h.13
= 33 Simplify.
The volume of the cone is 33 in.3.
Volumes of Pyramids and ConesLESSON 11-5
Additional Examples
Quick Check
GEOMETRYHELP
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 = = 2d2
V = r 2h Use the formula for the volume of a cone.13
V = (22)(7) Substitute 2 for r and 7 for h.13
About 29 cm3 of ice cream can fit entirely inside the cone.
Volumes of Pyramids and ConesLESSON 11-5
Additional Examples
Quick Check
Use a calculator.
