9-10 Measurement in Three-Dimensional Figures
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
9-10 Measurement in Three-Dimensional Figures
Warm Up
Fill in the blanks.
1. 1 yd = ___
36 in.
2. 1 mi  3.28
___ ft
3. 1 mi  ___
1.6 km
4. Find the surface are and volume of a cube with a
side length of 3 meters. 54 m2, 27 m3
9-10 Measurement in Three-Dimensional Figures
Problem of the Day
Chris cuts 1 in. by 1 in. squares from
the corners of an 8.5 in. by 11 in. paper
and fold the sides up to form an open
box. What is the volume of a box?
58.5 in2
9-10 Measurement in Three-Dimensional Figures
Sunshine State Standards
MA.8.G.5.1 Compare, contrast, and
convert units of measure between different
measurement systems (U.S. customary or
metric (SI)) and dimensions
including…area, volume, and derived units
to solve problems.
9-10 Measurement in Three-Dimensional Figures
You can convert units of area and volume. For
example, you can draw a diagram to help you
convert square feet to square inches.
You can convert units of area by squaring the
linear conversion factor.
9-10 Measurement in Three-Dimensional Figures
Additional Example 1: Converting Units of Measure
A shoebox has a length of 13 inches, a width
of 9 inches, and a height of 4 1/2 inches. Find
the surface area of the box in square
centimeters.
Step 1: Find the area in square inches.
A = lw
A = 13  9
A = lw
A = 9  4.5
A = lw
A = 13  4.5
A = 117 in2
A = 40.5 in2
A = 58.5 in2
A = 2(117 + 40.5 + 58.5) in2
A = 432 in2
Multiply each
area by 2.
9-10 Measurement in Three-Dimensional Figures
Additional Example 1 Continued
A shoebox has a length of 13 inches, a width
of 9 inches, and a height of 4 1/2 inches. Find
the surface area of the box in square
centimeters.
Step 2: Find the conversion factor for inches
to centimeters.
1 inch  2.54 cm
9-10 Measurement in Three-Dimensional Figures
Additional Example 1 Continued
A shoebox has a length of 13 inches, a width
of 9 inches, and a height of 4 1/2 inches. Find
the surface area of the box in square
centimeters.
Step 3: Convert the area.
Square the linear
conversion factor.
The surface area of the box in square centimeters is
2787.1 cm2.
9-10 Measurement in Three-Dimensional Figures
Check It Out: Example 1
A cone has a radius of 3 centimeters, a height
of 4 centimeters, and a slant height of 5
centimeters. What is the surface area of the
cone in square inches to the nearest tenth?
Use 3.14 for π.
S = 3.14(3)2 + 3.14(3)(5) = 28.26 + 47.1 = 75.36 cm2
2
1 in
75.36 cm2
= 11.68082336 in2
2.54 cm
The surface area of the cone is about 11.7 in2.
9-10 Measurement in Three-Dimensional Figures
Additional Example 2: Converting Units of Volume
A standard beverage can is a cylinder with a
radius of 3.25 cm and a height of 10.7 cm.
What is the volume of the can in cubic inches
to the nearest tenth?
Step 1: Find the volume in cubic centimeters.
V = r2h
 (3.14)(3.25)2(10.7)
 354.9 cm3
9-10 Measurement in Three-Dimensional Figures
Additional Example 2 Continued
A standard beverage can is a cylinder with a
radius of 3.25 cm and a height of 10.7 cm.
What is the volume of the can in cubic inches
to the nearest tenth?
Step 2: Convert the volume.
The volume of the can in cubic inches is about 21.7 in3.
9-10 Measurement in Three-Dimensional Figures
Check It Out: Example 2
Find the approximate volume of the cone in
cubic feet.
V = 1r2h
3
= 1 (3.14) (1)2 (2)
3
_
= 2.093 m3
_
2
1
ft
3
2.093 m
= 73.925369 ft3
0.3048m
The volume of the cone is about 73.9 ft3.
9-10 Measurement in Three-Dimensional Figures
Additional Example 3: Application
An archaeologist wants to apply a liquid
solution to the lateral area of a square
pyramid as a protectant. Each side of the
square base measures 12 meters and the slant
height is 10 meters. One gallon of solution
covers 200 ft2. About how many gallons of a
solution does the archaeologist need to cover
the lateral area of the pyramid?
Step 1: Find the lateral surface area of the pyramid.
9-10 Measurement in Three-Dimensional Figures
Additional Example 3 Continued
Step 2: Convert square meters to square feet.
1 m2  10.8 ft2, so 240 m2  2592 ft2.
Step 3: Find how many gallons of solution will
cover 2592 ft2.
= 12.96 gal
It will take about 13 gallons to cover the lateral
area of the pyramid.
9-10 Measurement in Three-Dimensional Figures
Check It Out: Example 3
The concrete tile shown is a hexagonal
prism. A cubic yard of concrete weighs
about 3600 pounds. What is the weight of
40 tiles in tons.
9-10 Measurement in Three-Dimensional Figures
Check It Out: Example 3 Continued
Volume of 1 tile in cubic feet:
6 • 1 (3)(2.6)(1) = 23.4 ft3
2
Volume in cubic yards:
3
1
yd
23.4 ft3
= 0.87 yd3
3 ft
0.87 yd3 • 3600 3lb = 3132 lb
1 yd
1 ton
1 tile: 3132 lb
= 1.57 tons
2000 lb
40 tiles: 40 • 1.57 tons = 62.8 tons
9-10 Measurement in Three-Dimensional Figures
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
9-10 Measurement in Three-Dimensional Figures
Lesson Quiz
1. A triangle has a base of 8 inches and a height of
22 inches. Find the area of the triangle in square
centimeters.  567.74 cm2
2. Find the volume of the pyramid
in cubic yards.
 671.41 yd3
3. A child is coloring a circle with a radius of 9
centimeters at a rate of 0.5 square inch per second.
How long will it take the child to color the circle? Use
3.14 for .  78.9 s
9-10 Measurement in Three-Dimensional Figures
Lesson Quiz for Student Response Systems
1. Convert.
1 mi3 = ___ yd3
A. 1760
B. 3,097,600
C. 5,451,776,000
D. 3
9-10 Measurement in Three-Dimensional Figures
Lesson Quiz for Student Response Systems
2. Find the volume.
A. 52 in3
B. 52 in2
C. 7800 in3
D. 7800 in2
9-10 Measurement in Three-Dimensional Figures
Lesson Quiz for Student Response Systems
3. Find the volume.
A. 7800 ft3
B. 650 ft3
C. 4.5 ft3
D. 54.2 ft3