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Intermediate Geometry : Solid Geometry

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Example Questions

Example Question #11 : Solid Geometry

If the surface area of a cube is 384 , what is the length of one side of the cube?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{384}{6}}$

Simplify.

$\text{side length}=\sqrt{64}$

Reduce.

$\text{side length}=8$

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Example Question #11 : How To Find The Length Of An Edge Of A Cube

If the surface area of a cube is 486 , find the length of one side of the cube.

Possible Answers:

Correct answer:

Explanation:

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{486}{6}}$

Simplify.

$\text{side length}=\sqrt{81}$

Reduce.

$\text{side length}=9$

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Example Question #12 : Solid Geometry

If the surface area of a cube is , find the length of one side of the cube.

Possible Answers:

$4\sqrt3$

$2\sqrt6$

$\sqrt{10}$

$6\sqrt2$

Correct answer:

$\sqrt{10}$

Explanation:

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{60}{6}}$

Simplify.

$\text{side length}=\sqrt{10}$

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Example Question #971 : Intermediate Geometry

If the surface area of a cube is 324 , find the length of one side of the cube.

Possible Answers:

$6\sqrt5$

$7\sqrt3$

$3\sqrt6$

$4\sqrt6$

Correct answer:

$3\sqrt6$

Explanation:

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{324}{6}}$

Simplify.

$\text{side length}=\sqrt{54}$

Reduce.

$\text{side length}=3\sqrt6$

Report an Error

Example Question #15 : Cubes

If the surface area of a cube is 168 , find the length of a side of the cube.

Possible Answers:

$10\sqrt2$

$6\sqrt3$

$2\sqrt7$

$7\sqrt3$

Correct answer:

$2\sqrt7$

Explanation:

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{168}{6}}$

Simplify.

$\text{side length}=\sqrt{28}$

Reduce.

$\text{side length}=2\sqrt7$

Report an Error

Example Question #12 : How To Find The Length Of An Edge Of A Cube

If the surface area of a cube is 120 , find the length of a side of the cube.

Possible Answers:

$4\sqrt2$

$2\sqrt5$

$2\sqrt6$

$2\sqrt7$

Correct answer:

$2\sqrt5$

Explanation:

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{120}{6}}$

Simplify.

$\text{side length}=\sqrt{20}$

Reduce.

$\text{side length}=2\sqrt5$

Report an Error

Example Question #11 : Solid Geometry

If the surface area of a cube is 192 , find the length of a side of the cube.

Possible Answers:

$8\sqrt2$

$4\sqrt2$

$12\sqrt2$

$3\sqrt2$

Correct answer:

$4\sqrt2$

Explanation:

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{192}{6}}$

Simplify.

$\text{side length}=\sqrt{32}$

Reduce.

$\text{side length}=4\sqrt2$

Report an Error

Example Question #13 : How To Find The Length Of An Edge Of A Cube

If the surface area of a cube is 540 , find the length of a side of the cube.

Possible Answers:

$3\sqrt{10}$

$10\sqrt3$

$2\sqrt{10}$

$4\sqrt{10}$

Correct answer:

$3\sqrt{10}$

Explanation:

Recall how to find the surface area of a cube:

$\text{Surface Area}=6(\text{side length})^2$

Since the question asks you to find the length of a side of this cube, rearrange the equation.

$\text{side length}^2=\frac{\text{Surface Area}}{6}$

$\text{side length}=\sqrt{\frac{\text{Surface Area}}{6}}$

Substitute in the given surface area to find the side length.

$\text{side length}=\sqrt{\frac{540}{6}}$

Simplify.

$\text{side length}=\sqrt{90}$

Reduce.

$\text{side length}=3\sqrt{10}$

Report an Error

Example Question #14 : How To Find The Length Of An Edge Of A Cube

A cubic swimming pool has edge lengths of $12\text{ meters}$ . In meters, how deep will the pool be if 864m^3 of water is added to the pool?

Possible Answers:

Correct answer:

Explanation:

We have the length, the width, and the volume for this cube. We just need to figure out the height.

Recall how to find the volume of a cube:

$\text{Volume of Cube}=\text{length}\times\text{width}\times\text{height}$

Normally, these three values would be the same. However, in this case, since the pool is not being filled up the entire way, the height of the cube will be different from its length and width.

$864=12\times12\times\text{height}$

$144(\text{height})=864$

$\text{height}=6$

The pool will be meters deep.

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Example Question #15 : How To Find The Length Of An Edge Of A Cube

If a cube has a volume of $343\;cm^3$ , what would be the length of the sides of the cube?

Possible Answers:

$7\;cm$

$9\;cm$

$6\;cm$

$8\;cm$

$10\;cm$

Correct answer:

$7\;cm$

Explanation:

A geometric cube has edges, all of equal length and the formula to solve for volume is:

$volume=length\cdot width\cdot height$

And since all edges are of equal length, we can use this formula to solve for length of sides:

$\\343\;cm^3=l\cdot l\cdot l\\ \\343\;cm^3=l^3\\ \\l=\sqrt[3]{343\;cm^3}=7\;cm$

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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #11 : Solid Geometry

Example Question #11 : How To Find The Length Of An Edge Of A Cube

Example Question #12 : Solid Geometry

Example Question #971 : Intermediate Geometry

Example Question #15 : Cubes

Example Question #12 : How To Find The Length Of An Edge Of A Cube

Example Question #11 : Solid Geometry

Example Question #13 : How To Find The Length Of An Edge Of A Cube

Example Question #14 : How To Find The Length Of An Edge Of A Cube

Example Question #15 : How To Find The Length Of An Edge Of A Cube

All Intermediate Geometry Resources

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