Lesson 12: Practice Problems

Problem 1

What is the volume of a cube with a side length of
- 4 centimeters?
- $\sqrt[3]{11}$ feet?
- $s$ units?
What is the side length of a cube with a volume of
- 1,000 cubic centimeters?
- 23 cubic inches?
- $v$ cubic units?

Problem 2

Write an equivalent expression that doesn’t use a cube root symbol.

$\sqrt[3]{1}$
$\sqrt[3]{216}$
$\sqrt[3]{8000}$
$\sqrt[3]{\frac{1}{64}}$
$\sqrt[3]{\frac{27}{125}}$
$\sqrt[3]{0.027}$
$\sqrt[3]{0.000125}$

Problem 3 From Unit 8 Lesson 11

Find the distance between each pair of points. If you get stuck, try plotting the points on graph paper.

$X = (5, 0)$ and $Y = (- 4, 0)$
$K = (- 21, - 29)$ and $L = (0, 0)$

Problem 4 From Unit 8 Lesson 9

Here is a 15-by-8 rectangle divided into triangles. Is the shaded triangle a right triangle? Explain or show your reasoning.

A rectangle with a point on the bottom side. Two line segments are drawn from the point to the top left vertex and from the point to the top right vertex of the rectangle creating 3 triangles. The left side of the rectangle is labeled 8. The segment from the bottom left corner of the rectangle to the point on the bottom side is labeled 9. The segment from the point on the bottom side to the bottom right corner is labeled 6. The middle triangle is shaded.

Problem 5 From Unit 8 Lesson 10

Here is an equilateral triangle. The length of each side is 2 units. A height is drawn. In an equilateral triangle, the height divides the opposite side into two pieces of equal length.

A triangle with a center height line drawn in. The side length is 2.

Find the exact height.
Find the area of the equilateral triangle.
(Challenge) Using $x$ for the length of each side in an equilateral triangle, express its area in terms of $x$ .