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ISEE Upper Level Math : Cubes

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

Example Questions

Example Question #2 : 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 $\displaystyle 343ft^3$, what is the length of one side of the cube?

Possible Answers:

14ft $\displaystyle 14ft$

49ft $\displaystyle 49ft$

7ft $\displaystyle 7ft$

49ft^2 $\displaystyle 49ft^2$

Correct answer:

7ft $\displaystyle 7ft$

Explanation:

There is a sculpture in front of town hall which is shaped like a cube. If it has a volume of $\displaystyle 343ft^3$, 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:

$V_{cube}=s^3$ $\displaystyle V_{cube}=s^3$

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

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

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

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

Possible Answers:

25m $\displaystyle 25m$

10m $\displaystyle 10m$

$\displaystyle 5m$

15m $\displaystyle 15m$

Correct answer:

$\displaystyle 5m$

Explanation:

You have a cube with a volume of 125 m^3 $\displaystyle 125 m^3$. 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.

$V_{cube}=s^3$ $\displaystyle V_{cube}=s^3$

$\displaystyle 125m^3=s^3$

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

Making our answer:

$\displaystyle 5m$

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Example Question #51 : Solid Geometry

Cube

The above cube has surface area 486. Evaluate $\displaystyle x$.

Possible Answers:

x =2 $\displaystyle x =2$

x = 16 $\displaystyle x = 16$

x = 63 $\displaystyle x = 63$

x = 9 $\displaystyle x = 9$

Correct answer:

x = 16 $\displaystyle x = 16$

Explanation:

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

$6s^{2} = A$ $\displaystyle 6s^{2} = A$

Substituting, then solving for $\displaystyle x$:

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

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

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

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

Since the sidelength is positive,

$\displaystyle x- 7 = 9$

x = 16 $\displaystyle x = 16$

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Example Question #5 : 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 $\displaystyle 216 m^3$, what is the length of one of the crate's dimension?

Possible Answers:

12 m $\displaystyle 12 m$

36m $\displaystyle 36m$

Not enough information to solve the equation.

6 m $\displaystyle 6 m$

Correct answer:

6 m $\displaystyle 6 m$

Explanation:

You have a crate with equal dimensions (height, length and width). If the volume of the cube is 216 m^3 $\displaystyle 216 m^3$, 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 $\displaystyle V=s^3$

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

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

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

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Example Question #6 : 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:

$\frac{10}{3}$ $\displaystyle \frac{10}{3}$

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

$\displaystyle 10$

$\sqrt[3]{30}$ $\displaystyle \sqrt[3]{30}$

$\sqrt{30}$ $\displaystyle \sqrt{30}$

Correct answer:

$\sqrt[3]{30}$ $\displaystyle \sqrt[3]{30}$

Explanation:

Write the formula to find the volume of a cube.

V=s^3 $\displaystyle V=s^3$

Substitute the volume into the equation.

30=s^3 $\displaystyle 30=s^3$

Cube root both sides.

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

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

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Example Question #371 : Geometry

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

Possible Answers:

20m $\displaystyle 20m$

25m $\displaystyle 25m$

$\displaystyle 5m$

10m $\displaystyle 10m$

15m $\displaystyle 15m$

Correct answer:

$\displaystyle 5m$

Explanation:

You have a cube with a volume of 125 m^3 $\displaystyle 125 m^3$. 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.

$V_{cube}=s^3$ $\displaystyle V_{cube}=s^3$

$\displaystyle 125m^3=s^3$

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

Making our answer:

$\displaystyle 5m$

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Cubes

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

All ISEE Upper Level Math Resources

Example Questions

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 #51 : Solid Geometry

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

Example Question #371 : Geometry

All ISEE Upper Level Math Resources

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