Cubed Roots
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by Devin Heller
| 9 Questions
Note from the author:
What is a cube root and how do I use this concept to find volume of prisms
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Find the surface area and the volume of the cube
The surface area of an object is the combined area of all of the sides on its surface. All six sides of a cube are congruent, so to find the surface area of a cube, all you have to do is find the surface area of one side of the cube and then multiply it by six.


Finding the volume of a cube is a snap! Generally, all that's needed is to multiply the cube's length × width × height. Since a cube's sides are all equal in length, another way of thinking of a cube's volume is s^3, where s is the length of one of the cube's sides.

The surface area of an object is the combined area of all of the sides on its surface. All six sides of a cube are congruent, so to find the surface area of a cube, all you have to do is find the surface area of one side of the cube and then multiply it by six.

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A different cube has a side of length 5.  Write two expressions that would represent how to find the volume of the cube.  One expression should use exponents.
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Now reverse the process.  If you know the volume, how long is the side?  Given the volumes of different cubes below.
a.) 8 cubic units
b.) 125 cubic meters
c.) 1000 cubic feet
d.) 40 cubic inches
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In problem 3 did you find the solution by guessing and checking, or did you find a special key on your calculator that helped?  Watch the video below to learn about the special cube root key on the graphing calculator
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The radical sign or radical symbol or root symbol is a symbol for the square root or higher-order root of a number.

What is an alternate method of finding the cube root without using the radical (root) symbol?
They showed you this in both videos. This is called Rewriting Radical Expressions Using Rational Exponents (exponents that are fractions)
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Just like with perfect squares and square roots, cube roots of perfect cubes are positive integers.  Some of them are listed below.
Without a calculator, you can approximate the cube root to be between consecutive integers, as you did with square roots. see example below



Approximate the following cube root below by using the perfect cubes below and above 100.  Write each answer in the same way as the above example.






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Use the perfet cube roots above and below 52 to approximate the cube root of 52.


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The office building where Ryan works is made up of two cube-shaped pieces.  At lunchtime, Ryan and his other office workers walk around the edge of the building for exercise.  If the volume of the larger part is 65,000 m3 and the volume of the smaller part is 4000 m3, what is the distance around the edge of the building?


How do you find the length of the side of a cube if you know its volume? What is this operation called? In your Notebook create examples that demonstrate what you know about cube roots and how to find them. Title this entry “Cube Root” and label it with today’s date.
Record How to find the length of the side of a cube if you know its volume?
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