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ISEE Upper Level Math : How to find the length of an edge of a cube

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All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Volume Of A Rectangular Solid

The volume of a cube is . What is the length of an edge of the cube?

Possible Answers:

Correct answer:

Explanation:

Let be the length of an edge of the cube. The volume of a cube can be determined by the equation:
x^3=V

x^3=64

$\sqrt[3]{x^3}=\sqrt[3]{64}$

x=4

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Example Question #1 : How To Find The Length Of An Edge Of A Cube

There is a sculpture in front of town hall which is shaped like a cube. If it has a volume of , what is the length of one side of the cube?

Possible Answers:

14ft

49ft^2

7ft

49ft

Correct answer:

7ft

Explanation:

There is a sculpture in front of town hall which is shaped like a cube. If it has a volume of , what is the length of one side of the cube?

To find the side length of a cube from its volume, simply use the following formula:

$V_{cube}=s^3$

Plug in what is known and use some algebra to get our answer:

$s=\sqrt[3]{343ft^3}=7ft$

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Example Question #2 : How To Find The Length Of An Edge Of A Cube

You have a cube with a volume of 125 m^3 . What is the cube's side length?

Possible Answers:

25m

10m

15m

Correct answer:

Explanation:

You have a cube with a volume of 125 m^3 . What is the cube's side length?

If we begin with the formula for volume of a cube, we can work backwards to find the side length.

$V_{cube}=s^3$

125m^3=s^3

$s=\sqrt[3]{125m^3}=5m$

Making our answer:

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Example Question #3 : How To Find The Length Of An Edge Of A Cube

Cube

The above cube has surface area 486. Evaluate .

Possible Answers:

x =2

x = 16

x = 9

x = 63

Correct answer:

x = 16

Explanation:

The surface area of a cube is six times the square of the length of each edge, which here is x- 7 . Therefore,

$6s^{2} = A$

Substituting, then solving for :

$6 (x-7)^{2} = 486$

$6 (x-7)^{2} \div 6 = 486 \div 6$

$(x-7)^{2} = 81$

$\sqrt{(x-7)^{2} }= \sqrt{81}$

Since the sidelength is positive,

x- 7 = 9

x = 16

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Example Question #4 : How To Find The Length Of An Edge Of A Cube

You have a crate with equal dimensions (height, length and width). If the volume of the cube is 216 m^3 , what is the length of one of the crate's dimension?

Possible Answers:

12 m

Not enough information to solve the equation.

6 m

36m

Correct answer:

6 m

Explanation:

You have a crate with equal dimensions (height, length and width). If the volume of the cube is 216 m^3 , what is the length of one of the crate's dimension?

Let's begin with realizing that we are dealing with a cube. A crate with equal dimensions will have equal height, length, and width, so it must be a cube.

With that in mind, we can find our side length by starting with the volume and working backward.

V=s^3

So, to find our side length, we just need to take the cubed root of the volume.

$s=\sqrt[3]{216m^3}=6m$

So, our answer is 6 meters, a fairly large crate!

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Example Question #5 : How To Find The Length Of An Edge Of A Cube

If the volume of a cube is 30, what must be the length of the edge of the cube?

Possible Answers:

$\frac{10}{3}$

$\sqrt{30}$

$\sqrt[3]{30}$

$\frac{\sqrt{10}}{3}$

Correct answer:

$\sqrt[3]{30}$

Explanation:

Write the formula to find the volume of a cube.

V=s^3

Substitute the volume into the equation.

30=s^3

Cube root both sides.

$\sqrt[3]{30}=\sqrt[3]{s^3}$

The answer is: $\sqrt[3]{30}$

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Example Question #6 : How To Find The Length Of An Edge Of A Cube

You have a cube with a volume of 125 m^3 . What is the cube's side length?

Possible Answers:

20m

25m

10m

15m

Correct answer:

Explanation:

You have a cube with a volume of 125 m^3 . What is the cube's side length?

If we begin with the formula for volume of a cube, we can work backwards to find the side length.

$V_{cube}=s^3$

125m^3=s^3

$s=\sqrt[3]{125m^3}=5m$

Making our answer:

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ISEE Upper Level Math : How to find the length of an edge of a cube

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : Volume Of A Rectangular Solid

Example Question #1 : How To Find The Length Of An Edge Of A Cube

Example Question #2 : How To Find The Length Of An Edge Of A Cube

Example Question #3 : How To Find The Length Of An Edge Of A Cube

Example Question #4 : How To Find The Length Of An Edge Of A Cube

Example Question #5 : How To Find The Length Of An Edge Of A Cube

Example Question #6 : How To Find The Length Of An Edge Of A Cube

All ISEE Upper Level Math Resources

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