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6-8 Accelerated 7 Unit 8 Lesson 12

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 •Lesson 12 Lesson 13 Lesson 14 Lesson 15

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IM K-5 Math
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Unit 8, Lesson 12

Edge Lengths, Volumes, and Cube Roots

Accelerated 7

Practice

Problem 1

What is the volume of a cube with an edge length of
1. 4 centimeters?
2. \(\sqrt[3]{11}\) feet?
3. \(s\) units?
What is the edge length of a cube with a volume of
1. 1,000 cubic centimeters?
2. 23 cubic inches?
3. \(v\) cubic units?

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Problem 2

Lesson 12 Resources

Student Materials

Find the positive solution to each equation. If the solution is irrational, write the solution using square root or cube root notation.

\(t^3=216\)
\(a^2=15\)
\(m^3=8\)
\(c^3=343\)
\(f^3=181\)

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Problem 3

For each cube root, find the two whole numbers that it lies between.

\(\sqrt[3]{11}\)
\(\sqrt[3]{80}\)
\(\sqrt[3]{120}\)
\(\sqrt[3]{250}\)

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Problem 4

Order the following values from least to greatest:

\(\displaystyle \sqrt[3]{530},\;\sqrt{48},\;\pi,\;\sqrt{121},\;\sqrt[3]{27},\;\frac{19}{2}\)

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Problem 5

ForLesson 2: Multiplying Powers of 10

Express each of the following as a single power of 10:

100
100,000
100,000,000
\(100 \boldcdot 10\)
\(1,000 \boldcdot 1,000\)

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Problem 6

ForLesson 7: A Proof of the Pythagorean Theorem

Find the value of each variable, in units, to the nearest tenth.

A triangle has a horizontal side labeled "d." The other two sides of the triangle are each labeled 11. A vertical dashed line extends from the vertex above the horizontal side to the horizontal side and is labeled 8. A right angle symbol is indicated between the vertical dashed line and the horizontal side.

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