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Five-Minute Check (over Lesson 125) CCSS Then/Now
New Vocabulary Key Concept Surface Area of a
Sphere Example 1 Surface Area of a
Sphere Example 2 Use Great Circles to Find
Surface Area Key Concept Volume of a
Sphere Example 3 Volumes of Spheres and
Hemispheres Example 4 Real-World Example Solve
Problems Involving Solids
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5-Minute Check 1
Find the volume of the cone. Round to the nearest
tenth if necessary.
A. 134.0 mm3 B. 157.0 mm3 C. 201.1 mm3 D. 402.1
mm3
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5-Minute Check 1
Find the volume of the cone. Round to the nearest
tenth if necessary.
A. 134.0 mm3 B. 157.0 mm3 C. 201.1 mm3 D. 402.1
mm3
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5-Minute Check 2
Find the volume of the pyramid. Round to the
nearest tenth if necessary.
A. 36 ft3 B. 125 ft3 C. 180 ft3 D. 270 ft3
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5-Minute Check 2
Find the volume of the pyramid. Round to the
nearest tenth if necessary.
A. 36 ft3 B. 125 ft3 C. 180 ft3 D. 270 ft3
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5-Minute Check 3
Find the volume of the cone. Round to the nearest
tenth if necessary.
A. 323.6 ft3 B. 358.1 ft3 C. 382.5 ft3 D. 428.1
ft3
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5-Minute Check 3
Find the volume of the cone. Round to the nearest
tenth if necessary.
A. 323.6 ft3 B. 358.1 ft3 C. 382.5 ft3 D. 428.1
ft3
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5-Minute Check 4
Find the volume of the pyramid. Round to the
nearest tenth if necessary.
A. 1314.3 in3 B. 1177.0 in3 C. 1009.4
in3 D. 987.5 in3
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5-Minute Check 4
Find the volume of the pyramid. Round to the
nearest tenth if necessary.
A. 1314.3 in3 B. 1177.0 in3 C. 1009.4
in3 D. 987.5 in3
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5-Minute Check 5
Find the volume of a cone with a diameter of 8.4
meters and a height of 14.6 meters.
A. 192.6 m3 B. 237.5 m3 C. 269.7 m3 D. 385.2 m3
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5-Minute Check 5
Find the volume of a cone with a diameter of 8.4
meters and a height of 14.6 meters.
A. 192.6 m3 B. 237.5 m3 C. 269.7 m3 D. 385.2 m3
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5-Minute Check 6
Find the height of a hexagonal pyramid with a
base area of 130 square meters and a volume of
650 cubic meters.
A. 12 m B. 15 m C. 17 m D. 22 m
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5-Minute Check 6
Find the height of a hexagonal pyramid with a
base area of 130 square meters and a volume of
650 cubic meters.
A. 12 m B. 15 m C. 17 m D. 22 m
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CCSS
Content Standards G.GMD.1 Give an informal
argument for the formulas for the circumference
of a circle, area of a circle, volume of a
cylinder, pyramid, and cone. G.GMD.3 Use volume
formulas for cylinders, pyramids, cones, and
spheres to solve problems. Mathematical
Practices 1 Make sense of problems and persevere
in solving them. 6 Attend to precision.
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Then/Now
You found surface areas of prisms and cylinders.

• Find surface areas of spheres.

• Find volumes of spheres.

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Vocabulary

• great circle
• pole
• hemisphere

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Concept
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Example 1
Surface Area of a Sphere
Find the surface area of the sphere. Round to
the nearest tenth.
S 4?r2 Surface area of a sphere 4?(4.5)2 Re
place r with 4.5. 254.5 Simplify.
Answer
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Example 1
Surface Area of a Sphere
Find the surface area of the sphere. Round to
the nearest tenth.
S 4?r2 Surface area of a sphere 4?(4.5)2 Re
place r with 4.5. 254.5 Simplify.
Answer 254.5 in2
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Example 1
Find the surface area of the sphere. Round to the
nearest tenth.
A. 462.7 in2 B. 473.1 in2 C. 482.6 in2 D. 490.9
in2
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Example 1
Find the surface area of the sphere. Round to the
nearest tenth.
A. 462.7 in2 B. 473.1 in2 C. 482.6 in2 D. 490.9
in2
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Example 2A
Use Great Circles to Find Surface Area
A. Find the surface area of the hemisphere.
Find half the area of a sphere with the radius of
3.7 millimeters. Then add the area of the great
circle.
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Example 2A
Use Great Circles to Find Surface Area
Surface area of a hemisphere
Replace r with 3.7.
129.0
Use a calculator.
Answer
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Example 2A
Use Great Circles to Find Surface Area
Surface area of a hemisphere
Replace r with 3.7.
129.0
Use a calculator.
Answer about 129.0 mm2
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Example 2B
Use Great Circles to Find Surface Area
B. Find the surface area of a sphere if the
circumference of the great circle is 10? feet.
First, find the radius. The circumference of a
great circle is 2?r. So, 2?r 10? or r 5.
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Example 2B
Use Great Circles to Find Surface Area
S 4?r2 Surface area of a sphere 4?(5)2 Repl
ace r with 5. 314.2 Use a calculator.
Answer
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Example 2B
Use Great Circles to Find Surface Area
S 4?r2 Surface area of a sphere 4?(5)2 Repl
ace r with 5. 314.2 Use a calculator.
Answer about 314.2 ft2
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Example 2C
Use Great Circles to Find Surface Area
C. Find the surface area of a sphere if the area
of the great circle is approximately 220 square
meters.
First, find the radius. The area of a great
circle is ?r2. So, ?r2 220 or r 8.4.
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Example 2C
Use Great Circles to Find Surface Area
S 4?r2 Surface area of a sphere 4?(8.4)2 Re
place r with 5. 886.7 Use a calculator.
Answer
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Example 2C
Use Great Circles to Find Surface Area
S 4?r2 Surface area of a sphere 4?(8.4)2 Re
place r with 5. 886.7 Use a calculator.
Answer about 886.7 m2
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Example 2A
A. Find the surface area of the hemisphere.
A. 110.8 m2 B. 166.3 m2 C. 169.5 m2 D. 172.8 m2
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Example 2A
A. Find the surface area of the hemisphere.
A. 110.8 m2 B. 166.3 m2 C. 169.5 m2 D. 172.8 m2
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Example 2B
B. Find the surface area of a sphere if the
circumference of the great circle is 8? feet.
A. 100.5 ft2 B. 201.1 ft2 C. 402.2 ft2 D. 804.3
ft2
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Example 2B
B. Find the surface area of a sphere if the
circumference of the great circle is 8? feet.
A. 100.5 ft2 B. 201.1 ft2 C. 402.2 ft2 D. 804.3
ft2
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Example 2C
C. Find the surface area of the sphere if the
area of the great circle is approximately 160
square meters.
A. 320 ft2 B. 440 ft2 C. 640 ft2 D. 720 ft2
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Example 2C
C. Find the surface area of the sphere if the
area of the great circle is approximately 160
square meters.
A. 320 ft2 B. 440 ft2 C. 640 ft2 D. 720 ft2
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Concept
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Example 3A
Volumes of Spheres and Hemispheres
A. Find the volume a sphere with a great circle
circumference of 30? centimeters. Round to the
nearest tenth.
Find the radius of the sphere. The circumference
of a great circle is 2?r. So, 2?r 30? or r 15.
Volume of a sphere
14,137.2 cm3 Use a calculator.
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Example 3A
Volumes of Spheres and Hemispheres
Answer
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Example 3A
Volumes of Spheres and Hemispheres
Answer The volume of the sphere is
approximately 14,137.2 cm3.
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Example 3B
Volumes of Spheres and Hemispheres
B. Find the volume of the hemisphere with a
diameter of 6 feet. Round to the nearest tenth.
The volume of a hemisphere is one-half the volume
of the sphere.
Volume of a hemisphere
Answer
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Example 3B
Volumes of Spheres and Hemispheres
B. Find the volume of the hemisphere with a
diameter of 6 feet. Round to the nearest tenth.
The volume of a hemisphere is one-half the volume
of the sphere.
Volume of a hemisphere
Answer The volume of the hemisphere is
approximately 56.5 cubic feet.
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Example 3A
A. Find the volume of the sphere to the nearest
tenth.
A. 268.1 cm3 B. 1608.5 cm3 C. 2144.7 cm3 D. 6434
cm3
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Example 3A
A. Find the volume of the sphere to the nearest
tenth.
A. 268.1 cm3 B. 1608.5 cm3 C. 2144.7 cm3 D. 6434
cm3
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Example 3B
B. Find the volume of the hemisphere to the
nearest tenth.
A. 3351.0 m3 B. 6702.1 m3 C. 268,082.6
m3 D. 134,041.3 m3
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Example 3B
B. Find the volume of the hemisphere to the
nearest tenth.
A. 3351.0 m3 B. 6702.1 m3 C. 268,082.6
m3 D. 134,041.3 m3
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Example 4
Solve Problems Involving Solids
ARCHEOLOGY The stone spheres of Costa Rica were
made by forming granodiorite boulders into
spheres. One of the stone spheres has a volume of
about 36,000? cubic inches. What is the diameter
of the stone sphere?
Understand You know that the volume of the
stone is 36,000? cubic inches. Plan First use
the volume formula to find the radius. Then find
the diameter.
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Example 4
Solve Problems Involving Solids
Replace V with 36,000?.

ENTER
(
)
2700
1
3
30
The radius of the stone is 30 inches. So, the
diameter is 2(30) or 60 inches.
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Example 4
Solve Problems Involving Solids
Answer
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Example 4
Solve Problems Involving Solids
Answer 60 inches
CHECK You can work backward to check
the solution.
?
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Example 4
RECESS The jungle gym outside of Jadas school
is a perfect hemisphere. It has a volume of
4,000? cubic feet. What is the diameter of the
jungle gym?
A. 10.7 feet B. 12.6 feet C. 14.4 feet D. 36.3
feet
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Example 4
RECESS The jungle gym outside of Jadas school
is a perfect hemisphere. It has a volume of
4,000? cubic feet. What is the diameter of the
jungle gym?
A. 10.7 feet B. 12.6 feet C. 14.4 feet D. 36.3
feet
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End of the Lesson