Transcript Interactive Chalkboard Chapter 7

Mathematics: Applications and Concepts, Course 3 Interactive Chalkboard
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Lesson 7-1 Area of Parallelograms, Triangles, and
Trapezoids
Lesson 7-2 Circumference and Area of Circles
Lesson 7-3 Area of Complex Figures
Lesson 7-4 Three-Dimensional Figures
Lesson 7-5 Volume of Prisms and Cylinders
Lesson 7-6 Volume of Pyramids and Cones
Lesson 7-7 Surface Area of Prisms and Cylinders
Lesson 7-8 Surface Area of Pyramids and Cones
Lesson 7-9 Precision and Significant Digits
Example 1 Find the Area of a Parallelogram
Example 2 Find the Area of a Triangle
Example 3 Find the Area of a Trapezoid
Example 4 Use Area to Solve a Real-Life Problem
Find the area of the parallelogram.
The base is 7 centimeters. The height is 2 centimeters.
Area of a parallelogram
Replace b with 7 and h with 2.
Multiply.
Answer: The area is 14 square centimeters.
Find the area of the parallelogram.
Answer:
Find the area of the triangle.
The base is 22 inches. The height is 4 inches.
Area of a triangle
Replace b with 22 and h with 4.
Multiply.
Multiply.
Answer: The area is 44 square inches.
Find the area of the triangle.
Answer:
Find the area of the trapezoid.
The height is 3.4 yards. The
lengths of the bases are 5
yards and 1 yard.
Area of a trapezoid
Replace h with 3.4,
and with 1.
with 5,
or 10.2
Simplify.
Answer: The area of the trapezoid is 10.2 square yards.
Find the area of the trapezoid.
Answer:
PAINTING A farmer plans to paint the triangular side
of a large shed, shown below. Find the area to be
painted. (Assume that no part of the window needs to
be painted.) If a gallon of paint covers 350 square
feet, how many gallons should the farmer buy?
To find the area to be painted,
subtract the area of the square
from the area of the triangle.
Area of triangle
Area of square
or 387.5
The area to be painted is 387.5 – 9 or 378.5 square feet.
If one gallon of paint covers 350 square feet, then the
farmer will need 378.5 350 or about 1.1 gallons. Since
the farmer cannot buy a fraction of a gallon, he will need
2 gallons.
Answer: 2 gallons
PAINTING Tyler plans to paint
his front door, shown at the
right. Find the area to be
painted. (Assume that no part
of the windows will be
painted.) If a quart of paint
covers 50 square feet, how
many quarts should Tyler
buy?
Answer:
1 qt
Example 1 Find the Circumferences of Circles
Example 2 Find the Circumferences of Circles
Example 3 Find the Areas of Circles
Example 4 Find the Areas of Circles
Example 5 Use Circumference and Area
Find the circumference of the circle. Round to the
nearest tenth.
Circumference of a circle
Replace d with 5.
This is the exact circumference.
Use a calculator to find
.5 x

ENTER
15.70796327
Answer: The circumference is about 15.7 feet.
Find the circumference of the circle. Round to the
nearest tenth.
Answer: 22.0 in.
Find the circumference of the circle. Round to the
nearest tenth.
Circumference of a circle
Replace r with 3.8.
Use a calculator.
Answer: The circumference is about 23.9 meters.
Find the circumference of the circle. Round to the
nearest tenth.
Answer: 22.6 m
Find the area of the circle. Round to the nearest tenth.
Area of a circle
Replace r with 3.
Evaluate
Use a calculator.
Answer: The area is about 28.3 square yards.
Find the area of the circle. Round to the nearest tenth.
Answer:
Find the area of the circle. Round to the nearest tenth.
Area of a circle
Replace r with half of
10 or 5.
Evaluate
Use a calculator.
Answer: The area is about 78.5 square inches.
Find the area of the circle. Round to the nearest tenth.
Answer:
POOLS The Patels have a
circular pool with a radius of
12 feet. They plan on installing
a 4-foot-wide walkway around
the pool. What will be the area
of the walkway?
To determine the area of the walkway, you must
subtract the area of the pool from the area of the outer
circle that includes the pool and the walkway.
Area of Outer Circle
Area of a circle
Replace r with 12
Evaluate
Use a calculator.
4 or 16.
Area of Pool
Area of a circle
Replace r with 12.
Evaluate
Use a calculator.
Area of Walkway
Area of Outer Circle – Area of Pool
Answer: The area of the walkway is about
351.9 square feet.
GARDENS The Shoemakers
have a circular pond with a
radius of 4 feet. They plan
on installing a 2-foot-wide
walkway around the pond.
What will be the area of the
walkway?
Answer:
Example 1 Find the Area of a Complex Figure
Example 2 Find the Area of a Complex Figure
Example 3 Use the Area of a Complex Figure
Find the area of the complex figure.
The figure can be separated into a rectangle and two
congruent triangles.
Area of rectangle
Area of one triangle
5
Answer: The area of the figure is
square inches.
Find the area of the complex figure.
Answer:
Find the area of the complex figure. Round to the
nearest tenth.
The figure can be separated into two semicircles and a
rectangle.
Area of one semicircle
Area of rectangle
Answer: The area of the figure is about
square centimeters.
Find the area of the complex figure. Round to the
nearest tenth.
Answer:
SHORT-RESPONSE TEST ITEM Below are plans for
the new deck on the Obwena’s house. How many
square feet of wood will be needed if one square
represents two square feet?
Read the Test Item
You need to find the area
of the deck in square
units and then multiply
this result by 2 to find the
area of the deck in square
feet.
Solve the Test Item
Find the area of the deck by dividing it into smaller areas.
Region A
Square
or 4
Region B
Triangle
or 2
Region C
Rectangle
or 6
Region D
Rectangle
or 8
Region E
Triangle
Region F
Rectangle
Region G
Triangle
Region H
Square
Answer: The total area is
or
square units. So, 2(36) or 72 square feet of
wood is needed to make the deck.
SHORT-RESPONSE TEST ITEM Below are plans for
the new patio to be added in the Murphy’s back yard.
How many square feet of concrete will need to be
poured if one square represents two square feet?
Answer:
Example 1 Identify Prisms and Pyramids
Example 2 Identify Prisms and Pyramids
Example 3 Analyze Real-Life Drawings
Example 4 Analyze Real-Life Drawings
Identify the solid. Name the number and shapes of
the faces. Then name the number of edges and
vertices.
Answer: The figure has two parallel congruent bases that
are octagons, so it is an octagonal prism. The
other faces are rectangles. It has a total of 10
faces, 24 edges, and 16 vertices.
Identify the solid. Name the number and shapes of
the faces. Then name the number of edges and
vertices.
Answer: triangular prism; 2 triangular faces, 3 rectangular
faces, 9 edges, and 6 vertices
Identify the solid. Name the number and shapes of
the faces. Then name the number of edges and
vertices.
Answer: The figure has one base that is a rectangle,
so it is a rectangular pyramid. The other
faces are triangles. It has a total of 5 faces,
8 edges, and 5 vertices.
Identify the solid. Name
the number and shapes of
the faces. Then name the
number of edges and
vertices.
Answer: pentagonal pyramid; 1 pentagonal base,
5 triangular faces, 10 edges, and 6 vertices
ARCHITECTURE The plans for a hotel fireplace are
shown below. Draw and label the top, front, and side
views.
Answer:
ARCHITECTURE
The plans for a
building are shown
to the right. Draw
and label the top,
front, and side
views.
Answer:
ARCHITECTURE The plans for a
hotel fireplace are shown to the
right. Each unit on the drawing
represents 1.5 feet. Find the area
of the floor covered by the
fireplace.
You can see from the front view that the floor is a
rectangle that is 5 units wide by 6 units long. The actual
dimensions are 5(1.5) feet by 6(1.5) feet or 7.5 feet by
9 feet.
Simplify.
Answer: The area of the floor covered by the fireplace is
67.5 square feet.
ARCHITECTURE The
plans for a building are
shown at the right. Each
unit on the drawing
represents 150 feet. Find
the area covered by the
second floor.
Answer:
Example 1 Find the Volume of a Rectangular Prism
Example 2 Find the Volume of a Triangular Prism
Example 3 Find the Volumes of Cylinders
Example 4 Find the Volumes of Cylinders
Example 5 Find the Volume of a Complex Solid
Find the volume of the prism.
Volume of a prism
The base is a rectangle, so
Simplify.
Answer: The volume is 385 cubic inches.
.
Find the volume of the prism.
Answer:
Find the volume of the prism.
Volume of a prism
The base is a triangle, so
The height of the prism is 4.
Simplify.
Answer: The volume is 270 cubic inches.
Find the volume of the prism.
Answer:
Find the volume of the cylinder.
Round to the nearest tenth.
Volume of a cylinder
Replace r with 3 and h with 12.
Simplify.
Answer: The volume is about 339.3 cubic centimeters.
Find the volume of the cylinder.
Answer:
Find the volume of the cylinder. Round to the nearest
tenth.
diameter of base, 18 yd; height, 25.4 yd
Since the diameter is 18 yards, the radius is 9 yards.
Volume of a cylinder
Replace r with 9 and h with 25.4.
Simplify.
Answer: The volume is about 6,463.5 cubic yards.
Find the volume of the cylinder. Round to the nearest
tenth.
diameter of base, 8 yd; height, 10 yd
Answer:
TOYS A wooden block has a single hole drilled
entirely through it. What is the volume of the block?
Round to the nearest hundredth.
The block is a rectangular
prism with a cylindrical hole.
To find the volume of the
block, subtract the volume
of the cylinder from the
volume of the prism.
Rectangular Prism
Cylinder
or 72
Answer: The volume of the box is about
cubic centimeters.
HOBBIES A small wooden
cube has been glued to a
larger wooden block for a
whittling project. What is
the volume of the wood to
be whittled?
Answer:
Example 1 Find the Volume of a Pyramid
Example 2 Use Volume to Solve a Problem
Example 3 Find the Volume of a Cone
Find the volume of the pyramid.
Volume of a pyramid
Simplify.
Answer: The volume is 140 cubic centimeters.
Find the volume of the pyramid.
Answer:
SOUVENIRS A novelty souvenir company wants to
make snow “globes” shaped like a pyramid. It decides
that the most cost-effective maximum volume of water
for the pyramids is 12 cubic inches. If a pyramid globe
measures 4 inches in height, find the area of its base.
Volume of a pyramid
Replace V with12 and h with 4.
Simplify.
Answer: The area of the base of the snow globe is
9 square inches.
TOYS A company is designing pyramid shaped
building blocks with a square base. They want the
volume of the blocks to be 18 square inches. If the
length of the side of the base is 3 inches, what should
be the height of the blocks?
Answer: 6 in.
Find the volume of the cone. Round
to the nearest tenth.
Volume of a cone
Replace r with1.5 and h with 8.
Simplify.
Answer: The volume is about 18.8 cubic meters.
Find the volume of the cone. Round to the nearest
tenth.
Answer:
Example 1 Surface Area of a Rectangular Prism
Example 2 Surface Area of a Triangular Prism
Example 3 Surface Area of a Cylinder
Find the surface area of the rectangular prism.
Write the formula.
Substitution.
Simplify.
Answer: The surface are is 606 square millimeters.
Find the surface area of the rectangular prism.
Answer:
CAMPING A family wants to reinforce the fabric of its
tent with a waterproofing treatment. Find the surface
area, including the floor, of the tent below.
A triangular prism consists of two congruent
triangular faces and three rectangular faces.
Draw and label a net of this prism.
Find the area of each face.
bottom
left side
right side
two bases
Add to find the total surface area.
Answer: The surface area of the tent is about
131.1 square feet.
DECORATING Julia is painting triangular prisms to
use as decoration in her garden. Find the surface
area of the prism.
Answer:
Find the surface area of the cylinder.
Round to the nearest tenth.
Surface area of a cylinder
Replace r with 2.5 and
h with 2.
Simplify.
Answer: The surface area is about
70.7 square meters.
Find the surface area of the cylinder. Round to the
nearest tenth.
Answer:
Example 1 Surface Area of a Pyramid
Example 2 Surface Area of a Cone
Find the surface area of the triangular pyramid.
Find the lateral area and the
area of the base.
Area of each lateral face
Area of a triangle
or 20
Replace b with 5 and h with 8.
There are 3 faces, so the lateral area is 3(20) or
60 square inches.
Area of base
Answer: The surface area of the pyramid is the sum of
the lateral area and the area of the base,
square inches.
Find the surface area of the square pyramid.
Answer:
Find the surface area of the cone.
Round to the nearest tenth.
Surface area of a cone.
Replace r with 1.5 and
Simplify.
Answer: The surface are of the cone is about
28.3 square meters.
Find the surface area of the cone.
Round to the nearest tenth.
Answer:
Example 1 Identify Precision Units
Example 2 Identify Significant Digits
Example 3 Identify Significant Digits
Example 4 Add Measurements
Example 5 Multiply Measurements
Identify the precision unit of the
thermometer.
Answer: There are 5 spaces between
each 10°mark, so the precision
unit is
of 10 degrees or 2 degrees.
Identify the precision unit of the ruler.
Answer:
inch
Determine the number of significant digits in the
measure 5,000 feet.
Answer: 1 significant digit
Determine the number of significant digits in the
measure 21.0 miles.
Answer: 3 significant digits
Determine the number of significant digits in the
measure 315.05 ounces.
Answer: 5 significant digits
Determine the number of significant digits in the
measure 35.006 centimeters.
Answer: 5 significant digits
MAIL Venita took four packages to the post office.
They weighed 1.27 pounds, 3.45 pounds, 0.524 pound,
and 2.7 pounds. Write the combined weight of her mail
using correct precision.
1.27
2 decimal places
3.45
2 decimal places
0.524
3 decimal places
1 decimal place
The least precise measurement
has 1 decimal place, so round
the sum to 1 decimal place.
7.944
Answer: The combined weight of the packages is about
7.9 pounds.
DELI Veric bought 1.5 pounds of turkey, 0.75 pound of
roast beef, 2.4 pounds of ham, and 0.5 pound of
salami. Write the combined weight of the lunch meat
that Veric bought using correct precision.
Answer: 5.2 lb
Use the correct number of significant
digits to find the volume of the
cylinder. Use 3.14 for pi.
Volume of a cylinder
The height of the cylinder has
the least number of significant
digits, 2.
Answer: Round the answer, 187.0017188, so that it has
2 significant digits. The volume of the cylinder is
about 190 cubic inches.
Use the correct number of significant digits to find
the volume of the rectangular prism.
Answer:
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