Texas Math, Course 3

Chapter 7 Connect Algebra to Geometry

Lesson 7-1 Volume of Cylinders

Page 479

Determine the volume of the cylinder. Round to the nearest tenth.

2

2

3

Volume of a cylinder

The base is a circl

(π )

π(3) (5)

e.

Replace with 3 and w

141.4 i

ith 5.

Simpln ify.

V Bh

V r

h

h

V

V

r

Mia’s parents have a cylindrical oak tree stump that has a diameter of 3

feet and a height of 2 feet. How much does the stump weigh if the average

weight of oak is 59 pounds per cubic foot? Round to the nearest tenth.

First find the volume of the stump.

2

2

3

Volume of a cylinder

The base is a circle.

Replace with 1.5 and with 2.

Si

(π )

π(1.5) (2)

14.1 ft p f . m li y

r

V Bh

h

V r h

V

V

To find the weight of the stump, multiply the volume by 59.

14.1(59) = 831.9

So, the weight of the stump is about 831.9 pounds.

Texas Math, Course 3

Chapter 7 Connect Algebra to Geometry

Lesson 7-2 Volume of Cones

Pages 491-492

Determine the volume of a cone with a height of 8.4 feet and a diameter of

3.5 feet. Round to the nearest tenth.

2

2

3

Volume of a cone

Replace with 1.75 and

1π

with 8.4.

Simpl

3

1π(1.75) (8.4)

ify

3

26.9 ft .

r h

V r h

V

V

A cylinder has a radius of 5 centimeters and a height of 12 centimeters.

What would the height of a cone need to be if it has the same volume and

radius? Round to the nearest centimeter.

Let h be the height of the cylinder, H be the height of the cone, and r be the

radius of both.

2 2

2 2

1π π

3

1π(5) (12) π(5)

The volume of the cylinder is equal to the volume of the cone.

Replace 3

1300π = (25)π

with 5 and with 12.

Sim 3

900π = 25π

plify.

Multiply b

r r

r

H

H

h

h

H

H

oth sides by 3.

Divide each side by 25π.900π 25π

= 25π 25π

36 Si y mplif .

H

H

The height of the cone is 36 centimeters.

Texas Math, Course 3

Chapter 7 Connect Algebra to Geometry

Lesson 7-3 Volume of Spheres

Page 499

Determine the volume of the sphere. Round to the

nearest tenth.

3

3

3

Volume of a sphere

Replace with 7.2

4π

3

4π(7.2)

3

1,5

.

Simplify. 63. Use5 in a calculator .

V r

rV

V

The radius of a basketball is 4.7 inches. What is the volume of the

basketball? Round to the nearest tenth.

3

3

Volume of a sphere

Replace with 4.7.

4π

3

4π(4.7)

3

434. Simplify. Use a calculat9 o r.

V r

V

V

r

The volume of the basketball is about 434.9 cubic inches.

Texas Math, Course 3

Chapter 7 Connect Algebra to Geometry

Lesson 7-4 Surface Area of Prisms

Page 515

Determine the lateral and surface area of the rectangular prism. Round to

the nearest tenth if necessary.

Determine the lateral area.

L.A. = Ph Lateral area of a rectangular prism

L.A. = (9 + 5 + 9 + 5)8 Replace P with the perimeter of the base and h with 8.

L.A. = 224 Simplify.

The lateral area is 224 square centimeters.

Determine the surface area.

S = Ph + 2B Surface area of a rectangular prism

S = 224 + 2(9 • 5) Replace Ph with 224 and B with the area of the base.

S = 314 Simplify.

The surface area is 314 square centimeters.

When making a book cover, Anwar uses enough material to cover the front,

back, and spine of the book. He adds 20 square inches more to the surface

area to allow for overlap. How many square inches of paper will Anwar use

to make a book cover for a book 11 inches long, 8 inches wide, and 1 inch

high?

Determine the surface area of the book Anwar needs to cover by finding the

surface area of the front, back, and spine of the book. Then add 20 square inches.

The surface area of the front, back, and spine is (11)(8) + (11)(8) + (11)(1) or 187

square inches. So, Anwar will use 187 + 20 or 207 square inches of paper to

make the book cover.

2

1

2

3

Texas Math, Course 3

Chapter 7 Connect Algebra to Geometry

Lesson 7-5 Surface Area of Cylinders

Page 525

Determine the total surface area of the cylinder. Round to the nearest tenth.

2

2

2

2π 2π

2π(2)(5) 2π(2)

Surface area of a cylinder

Replace with

88.0 mm

2 and with 5.

Simplify .

S rh

r

r

S

hS

Determine the lateral area of a cylindrical copper pipe that has a diameter

of 6.4 inches and a height of 12 inches. Round to the nearest tenth.

. . 2π

. . 2π(3.2)(12)

Lateral area of a cylinder

Replace with 3

. .

.2 and with 12

241

.

Simp.3 lify.

L A rh

L A h

A

r

L

The lateral area of the pipe is about 241.3 square inches.

Texas Math, Course 3

Chapter 7 Connect Algebra to Geometry

Lesson 7-6 Changes in Dimensions

Pages 535-536

A cereal box has a surface area of 280 square inches. What is the surface

area of a similar box with dimensions that are larger by a scale factor of

1.4?

2. . 280 1.4

. . 280 1.96

Multiply by the square of the scale factor.

. . 548.8

Squ

are 1.4.

Simplify.

S A

S A

S A

The surface area of the larger box is 548.8 square inches.

Use a Problem-Solving Model Two spheres are similar in shape. The scale

factor between the smaller sphere and the larger sphere is 3

4. If the volume

of the smaller sphere is 126.9 cubic meters, what is the volume of the larger

sphere?

The scale factor between the larger sphere and the smaller sphere is 4

3.

3

Multiply by the cube of the scale factor.4

126.9 3

64126.9

4Cube .

3

27

300.8 Simplify.

V

V

V

The volume of the larger sphere is 300.8 cubic meters.