Transcript Glencoe Geometry - Burlington County Institute of Technology

Five-Minute Check (over Lesson 12–4)
CCSS
Then/Now
Key Concept: Volume of a Pyramid
Example 1: Volume of a Pyramid
Key Concept: Volume of a Cone
Example 2: Volume of a Cone
Example 3: Real-World Example: Find Real-World Volumes
Concept Summary: Volumes of Solids
Over Lesson 12–4
Find the volume of the prism. Round to the nearest
tenth if necessary.
A. 240 in3
B. 200 in3
C. 120 in3
D. 100 in3
Over Lesson 12–4
Find the volume of the cylinder. Round to the
nearest tenth if necessary.
A. 785.4 cm3
B. 547.3 cm3
C. 314.2 cm3
D. 157.1 cm3
Over Lesson 12–4
What is the volume of the cylinder. Round to the
nearest tenth if necessary.
A. 627.5 m3
B. 843.4 m3
C. 986.4 m3
D. 1017.9 m3
Over Lesson 12–4
What is the volume of the prism? Round to the
nearest tenth if necessary.
A. 225.4 ft3
B. 203.7 ft3
C. 183.8 ft3
D. 152.8 ft3
Over Lesson 12–4
Find the volume of a rectangular prism with a
length of 12 yards, a width of 14 yards, and a
height of 9 yards.
A. 1110 yd3
B. 1227 yd3
C. 1512 yd3
D. 2012 yd3
Over Lesson 12–4
The volume of a triangular prism is 655 cubic feet.
The height of the prism is 5 feet. Find the area of
one triangular base.
A. 65.5 ft2
B. 131 ft2
C. 650 ft2
D. 660 ft2
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.
7 Look for and make use of structure.
You found surface areas of pyramids and
cones.
• Find volumes of pyramids.
• Find volumes of cones.
Volume of a Pyramid
Find the volume of the square pyramid.
Volume of a pyramid
s
21
3, h
7
Multiply.
Answer: The volume of the pyramid is 21 cubic inches.
Brad is building a model pyramid for a social
studies project. The model is a square pyramid
with a base edge of 8 feet and a height of 6.5 feet.
Find the volume of the pyramid.
A. 416 ft3
B.
C.
D.
Volume of a Cone
A. Find the volume of the oblique cone to the
nearest tenth.
Volume of a Cone
Volume of a cone
r = 9.1, h = 25
≈ 2168.0
Use a calculator.
Answer: The volume of the cone is approximately
2168.0 cubic feet.
Volume of a Cone
B. Find the volume of the cone to the nearest tenth.
Volume of a Cone
Volume of a cone
r = 5, h = 12
≈ 314.2
Use a calculator.
Answer: The volume of the cone is approximately
314.2 cubic inches.
A. Find the volume of the oblique
cone to the nearest tenth.
A. 444.4 m3
B. 27,463.2 m3
C. 3051.5 m3
D. 9154.4 m3
B. Find the volume of the cone to the nearest tenth.
A. 3015.9 m3
B. 125.7 m3
C. 1005.3 m3
D. 251.3 m3
Find Real-World Volumes
SCULPTURE At the top of a stone tower is a
pyramidion in the shape of a square pyramid. This
pyramid has a height of 52.5 centimeters and the
base edges are 36 centimeters. What is the volume
of the pyramidion? Round to the nearest tenth.
Volume of a pyramid
B = 36 ● 36, h = 52.5
Simplify.
Answer: The volume of the pyramidion is 22,680 cubic
centimeters.
SCULPTURE In a botanical garden is a silver
pyramidion in the shape of a square pyramid. This
pyramid has a height of 65 centimeters and the
base edges are 30 centimeters. What is the volume
of the pyramidion? Round to the nearest tenth.
A. 18,775 cm3
B. 19,500 cm3
C. 20,050 cm3
D. 21,000 cm3