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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #9 : Cubes

If the surface area of a cube is 864 , find the length of a 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.

$\text{side length}=\sqrt{\frac{864}{6}}$

Simplify.

$\text{side length}=\sqrt{144}$

Reduce.

$\text{side length}=12$

Report an Error

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

If the surface area of a cube is 750 , find the length of a side of the cube.

Possible Answers:

$6\sqrt6$

$7\sqrt7$

$4\sqrt2$

$5\sqrt5$

Correct answer:

$5\sqrt5$

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.

$\text{side length}=\sqrt{\frac{750}{6}}$

Simplify.

$\text{side length}=\sqrt{125}$

Reduce.

$\text{side length}=5\sqrt5$

Report an Error

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

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.

$\text{side length}=8$

Report an Error

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.

$\text{side length}=9$

Report an Error

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

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

Possible Answers:

$\sqrt{10}$

$6\sqrt2$

$2\sqrt6$

$4\sqrt3$

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.

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

Report an Error

Example Question #11 : Cubes

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

Possible Answers:

$4\sqrt6$

$3\sqrt6$

$7\sqrt3$

$6\sqrt5$

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 #11 : Solid Geometry

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

Possible Answers:

$6\sqrt3$

$10\sqrt2$

$2\sqrt7$

$7\sqrt3$

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:

$3\sqrt2$

$12\sqrt2$

$4\sqrt2$

$8\sqrt2$

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

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All Intermediate Geometry Resources

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #9 : Cubes

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

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

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

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

Example Question #11 : Cubes

Example Question #11 : Solid Geometry

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

All Intermediate Geometry Resources

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