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ISEE Upper Level Math : Geometry

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

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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 #2 : How To Find The Surface Area Of A Cube

While exploring an ancient ruin, you discover a small puzzle cube. You measure the side length to be . Find the cube's surface area.

Possible Answers:

866cm^3

144cm^3

864cm^2

1728 cm^2

Correct answer:

864cm^2

Explanation:

While exploring an ancient ruin, you discover a small puzzle cube. You measure the side length to be . Find the cube's surface area.

To find the surface area, use the following formula:

SA=6s^2=6(12cm)^2=864cm^2

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Example Question #41 : Solid Geometry

Find the surface area of a cube with a base of 8in.

Possible Answers:

$384\text{in}^2$

$48\text{in}^2$

$336\text{in}^2$

$212\text{in}^2$

$128\text{in}^2$

Correct answer:

$384\text{in}^2$

Explanation:

A cube has all equal sides (length, width, height). To find the surface area of a cube, we will use the following formula:

SA = 6a^2

Now, we know the base of the cube is 8in. Because all sides are equal (i.e. all sides are 8in), we will use that to substitute into the formula. We get

$SA = 6 \cdot (8\text{in})^2$

$SA = 6 \cdot 64\text{in}^2$

$SA = 384\text{in}^2$

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Example Question #42 : Solid Geometry

You are building a box to hold your collection of rare rocks. You want to build a cube-shaped box with a side length of 3 feet. If you do so, what will the surface area of your box be?

Possible Answers:

18ft^2

54 ft^2

60 ft^2

27ft^2

Correct answer:

54 ft^2

Explanation:

You are building a box to hold your collection of rare rocks. You want to build a cube-shaped box with a side length of 3 feet. If you do so, what will the surface area of your box be?

To find the surface area, use the formula:

SA=6s^2

Where s is our side length and SA is our surface area.

Plug in our known and simplify

SA=6 (3ft)^2=6*9ft^2=54ft^2

So, our answer is

54ft^2

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Example Question #363 : Geometry

Find the surface area of a cube with a length of 11in.

Possible Answers:

$512\text{in}^2$

$726\text{in}^2$

$649\text{in}^2$

$121\text{in}^2$

$44\text{in}^2$

Correct answer:

$726\text{in}^2$

Explanation:

To find the surface area of a cube, we will use the following formula:

SA = 6a^2

where a is the length of any side of the cube. Because it is a cube, all sides are equal. Therefore, we can use any side in the formula.

Now, we know the length of the cube is 11in. We can substitute that into the formula. We get

$SA = 6 \cdot (11\text{in})^2$

$SA = 6 \cdot 121\text{in}^2$

$SA = 726\text{in}^2$

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Example Question #45 : Solid Geometry

Find the surface area of a cube with a width of 7cm.

Possible Answers:

$343\text{cm}^2$

$368\text{cm}^2$

$294\text{cm}^2$

$\text{There is not enough information to solve the problem.}$

$442\text{cm}^2$

Correct answer:

$294\text{cm}^2$

Explanation:

To find the surface area of a cube, we will use the following formula.

SA = 6a^2

where a is the length of any side of the cube. We can use any side because all sides have the same length on a cube.

Now, we know the width of the cube is 7cm. So, we can substitute. We get

$SA = 6 \cdot (7\text{cm})^2$

$SA = 6 \cdot 49\text{cm}^2$

$SA = 294\text{cm}^2$

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Example Question #51 : Solid Geometry

Find the surface area of a cube with a width of 7in.

Possible Answers:

$294\text{in}^2$

$84\text{in}^2$

$147\text{in}^2$

$245\text{in}^2$

$343\text{in}^2$

Correct answer:

$294\text{in}^2$

Explanation:

To find the surface area of a cube, we will use the following formula.

SA = 6a^2

where a is the length of any side of the cube.

Now, we know the width of the cube is 7in. Because it is a cube, all sides are equal (this is why we can use any length in the formula). So, we will use 7in in the formula. We get

$SA = 6 \cdot (7\text{in})^2$

$SA = 6 \cdot 49\text{in}^2$

$SA = 294\text{in}^2$

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Example Question #51 : Solid Geometry

Find the surface area of a cube with a width of 6in.

Possible Answers:

$72\text{in}^2$

$27\text{in}^2$

$432\text{in}^2$

$216\text{in}^2$

$144\text{in}^2$

Correct answer:

$216\text{in}^2$

Explanation:

To find the surface area of a cube, we will use the following formula:

$SA = 6 \cdot l \cdot w$

where l is the length, and w is the width of the cube.

Now, we know the width of the cube is 6in. Because it is a cube, all lengths, widths, and heights are the same. Therefore, the length is also 6in.

Knowing this, we can substitute into the formula. We get

$SA = 6 \cdot 6\text{in} \cdot 6\text{in}$

$SA = 6 \cdot 36\text{in}^2$

$SA = 216\text{in}^2$

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Example Question #52 : Solid Geometry

Find the surface area of a cube with a length of 9cm.

Possible Answers:

$338\text{cm}^2$

$576\text{cm}^2$

$486\text{cm}^2$

$324\text{cm}^2$

$218\text{cm}^2$

Correct answer:

$486\text{cm}^2$

Explanation:

To find the surface area of a cube, we will use the following formula:

SA = 6 a^2

where a is the length of one side of the cube.

Now, we know the length of the cube is 9cm. So, we get

$SA = 6 \cdot (9\text{cm})^2$

$SA = 6 \cdot 81\text{cm}^2$

$SA = 486\text{cm}^2$

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Example Question #52 : Solid Geometry

Find the surface area of a cube with a width of 6cm.

Possible Answers:

$428\text{cm}^2$

$96\text{cm}^2$

$216\text{cm}^2$

$128\text{cm}^2$

$361\text{cm}^2$

Correct answer:

$216\text{cm}^2$

Explanation:

To find the surface area of a cube, we will use the following formula.

SA = 6a^2

where a is the length of any side of the cube.

Now, we know the width of the cube is 6cm.

So, we get

$SA = 6 \cdot (6\text{cm})^2$

$SA = 6 \cdot 6\text{cm}^2$

$SA = 216\text{cm}^2$

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Example Question #2 : 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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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Geometry

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 Surface Area Of A Cube

Example Question #41 : Solid Geometry

Example Question #42 : Solid Geometry

Example Question #363 : Geometry

Example Question #45 : Solid Geometry

Example Question #51 : Solid Geometry

Example Question #51 : Solid Geometry

Example Question #52 : Solid Geometry

Example Question #52 : Solid Geometry

Example Question #2 : Volume Of A Rectangular Solid

All ISEE Upper Level Math Resources

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