Volume of Pyramids & Cones

Section 11-5

Volume of a Pyramid

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.

Volume of Pyramids and Cones

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.

Volume of Pyramids and Cones

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.

Volume of Pyramids and Cones

(continued)

10-6

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

Volume of Pyramids and ConesGEOMETRY LESSON 10-6

10-6

(continued)

Volume of a Cone

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.

Volume of Pyramids and Cones

The volume of the cone is 33 in.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 = = 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

29.321531 Use a calculator.

About 29 cm3 of ice cream can fit entirely inside the cone.

Volume of Pyramids and Cones