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Study Guide ReviewUNIT 5
Study Guide ReviewKey Vocabularyalternate exterior angles
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Manuel’s house
Thomas’s houseSchool
9 mi
5 mi
10 ft
10 ft
s
r h = 10 cm
w = 10 cmℓ = 25 cm
7 in.18 in.
b
Thomas drew a diagram to represent the location of his house, the school, and his friend Manuel’s house. What is the distance from the school to Manuel’s house? Round your answer to the nearest tenth.
EXERCISESFind the missing side lengths. Round your answers to the nearest hundredth. (Lesson 12.1)
1.
2.
EXAMPLE 2
a2 + b2 = c2
52 + 92 = c2
25 + 81 = c2
c2 = 106
c = √_
106 ≈ 10.3
The distance from the school to Manuel’s house is about 10.3 miles.
The Pythagorean Theorem
How can you use the Pythagorean Theorem to solve real-world problems?
Find the missing side length. Round your answer to the nearest tenth.
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5 ft
7.5 ft
xO 4
4
2
-2
-4
-2-4
y
A B
C
Key Vocabularycone (cono)
cylinder (cilindro)
sphere (esfera)
Volume
How can you solve real-world problems that involve volume?
Find the volume of the cistern. Round your answer to the nearest hundredth. Use 3.14 for π.
V = πr 2h
≈ 3.14 ⋅ 2.52 ⋅ 7.5
≈ 3.14 ⋅ 6.25 ⋅ 7.5
≈ 147.19
The cistern has a volume of approximately 147.19 cubic feet.
Find the volume of a sphere with a radius of 3.7 cm. Write your answer in terms of π and to the nearest hundredth.
The volume of the sphere is approximately 67.54π cm3, or 212.07 cm3.
MODULE1313? ESSENTIAL QUESTION
Find the volume of the cistern. Round your answer to the nearest
EXAMPLE 1
EXAMPLE 2
V = 4 _ 3 πr 3
≈ 4 _ 3 ⋅ π ⋅ 3.73
≈ 4 _ 3 ⋅ π ⋅ 50.653
≈ 67.54π
V = 4 _ 3 πr 3
≈ 4 _ 3 ⋅ 3.14 ⋅ 3.73
≈ 4 _ 3 ⋅ 3.14 ⋅ 50.653
≈ 212.07
3. Hye Sun has a modern coffee table whose top is a triangle with the following side lengths: 8 feet, 3 feet, and 5 feet. Is Hye Sun’s coffee table top a right triangle? (Lesson 12.2)
4. Find the length of each side of triangle ABC. If necessary, round your answers to the nearest hundredth. (Lesson 12.3)