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Surface Areas of Pyramids and Cones
Lesson 11-3
Geometry
Lesson Quiz
1. Find the slant height of a square pyramid with base edges 12 cm and
altitude 8 cm. 10 cm
2. Find the lateral area of the regular
square pyramid to the right.
56 in.2
3. Find the surface area of the pyramid to the right
whose base is a regular hexagon. Round to
the nearest whole number. 1517 ft2
4. Find the surface area of a cone with radius 8 cm and slant height 17
cm in terms of . 200 cm2
5. The roof of a building is shaped like a cone with diameter 40 ft and
height 20 ft. Find the area of the roof. Round to the nearest whole
1777 ft2
number.
Lesson
Main
Lesson
11-4
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Check Skills You’ll Need
(For help, go to Lessons 1-9 and 10-1.)
Find the area of each figure. Round to the nearest tenth if necessary.
1. square - side length 7 cm
2. circle - diameter 15 in.
A = r2 = (7.5)2 = 56.25 ≈ 176.7 in.2
A = s2 = 72 = 49 cm2
3. circle - radius 10 mm
4. rectangle - 3 ft by 1 ft
A = lw = (3)(1) = 3 ft2
A = r2 = (10)2 = 100 ≈ 314.2 mm2
5. rectangle - 14 in. by 11 in.
6. triangle - base 11 cm, height 5 cm
A = lw = (14)(11) = 154 in.2
A = ½ bh = ½ (11)(5) = 27.5 cm2
7. equilateral triangle - side length 8 in.
A = ½ bh = ½ (8)(4
3) = 16
3 ≈ 27.7 in.2
Check Skills You’ll Need
Lesson
Main
Lesson
11-4
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Notes
The volume of a three-dimensional figure is the
number of nonoverlapping unit cubes of a given size
that will exactly fill the interior.
Cavalieri’s principle says that if two threedimensional figures have the same height and have
the same cross-sectional area at every level, they
have the same volume.
The area of each
shaded cross section
below is 6 cm2. Since
the prisms have the
same height, their
volumes must be the
same.
Lesson
Main
Lesson
11-4
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Notes
Lesson
Main
Lesson
11-4
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Additional Examples
Finding Volume of a Rectangular Prism
Find the volume of the prism below.
The area of the base B =
V = Bh
w = 3  5 = 15.
Use the formula for volume.
= 15 • 5
Substitute 15 for B and 5 for h.
= 75
Simplify.
The volume of the rectangular prism is 75 in.3.
Quick Check
Lesson
Main
Lesson
11-4
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Additional Examples
Finding Volume of a Triangular Prism
Find the volume of the prism below.
The prism is a right triangular prism with triangular bases.
The base of the triangular prism is a right triangle where one leg is the
base and the other leg is the altitude.
Use the Pythagorean Theorem to calculate the length of the other leg.
292 – 202 =
Lesson
Main
841  400 =
441  21
Lesson
11-4
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Additional Examples
(continued)
1
1
The area B of the base is 2 bh = 2 (20)(21) = 210. Use the area of the
base to find the volume of the prism.
V = Bh
Use the formula for the volume of a prism.
= 210 • 40
Substitute.
= 8400
Simplify.
The volume of the triangular prism is 8400 m3.
Quick Check
Lesson
Main
Lesson
11-4
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Additional Examples
Finding Volume of a Cylinder
Find the volume of the cylinder below. Leave your answer in
terms of .
The formula for the volume of a cylinder is V =
shows h and d, but you must find r.
r 2h. The diagram
1
r = 2d=8
V=
=
r 2h
• 82 • 9
= 576
Use the formula for the volume of a cylinder.
Substitute.
Simplify.
The volume of the cylinder is 576
Lesson
Main
ft3.
Lesson
11-4
Quick Check
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Additional Examples
Finding Volume of a Composite Figure
Find the volume of the composite space figure.
You can use three rectangular prisms to find the volume.
Each prism’s volume can be found using the formula V = Bh.
Lesson
Main
Lesson
11-4
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Additional Examples
(continued)
Volume of prism I = Bh = (14 • 4) • 25 = 1400
Volume of prism II = Bh = (6 • 4) • 25 = 600
Volume of prism III = Bh = (6 • 4) • 25 = 600
Sum of the volumes = 1400 + 600 + 600 = 2600
The volume of the composite space figure is 2600 cm3.
Quick Check
Lesson
Main
Lesson
11-4
Feature
Geometry
Lesson
Main
Lesson
Feature
Geometry
Lesson
Main
Lesson
Feature
Volumes of Prisms and Cylinders
Lesson 11-4
Geometry
Lesson Quiz
Find the volume of each figure to the nearest whole number.
1.
2.
3.
62 m3
1800 ft3
4.
45 in.3
5.
63 m3
Lesson
Main
1800 mm3
Lesson
11-4
Feature