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ISEE Upper Level Math : Solid Geometry

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

Example Questions

Example Question #1 : How To Find The Surface Area Of A Cube

One of your holiday gifts is wrapped in a cube-shaped box.

If one of the edges has a length of 6 inches, what is the surface area of the box?

Possible Answers:

96in^2

36in^2

216in^3

216in^2

Correct answer:

216in^2

Explanation:

One of your holiday gifts is wrapped in a cube-shaped box.

If one of the edges has a length of 6 inches, what is the surface area of the box?

We can find the surface area of a square by squaring the length of the side and then multiplying it by 6.

$SA_{square}=6s^2=6(6in)^2=216in^2$

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Example Question #353 : Geometry

Find the surface area of a cube that has a width of 6cm.

Possible Answers:

$36\text{cm}^2$

$108\text{cm}^2$

$72\text{cm}^2$

$216\text{cm}^2$

$125\text{cm}^2$

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. Because it is a cube, all sides are 6cm. That is why we can choose any side to substitute into the formula.

Now, knowing this, we can substitute into the formula. We get

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

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

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

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Example Question #354 : Geometry

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

Possible Answers:

$649\text{in}^2$

$294\text{in}^2$

$49\text{in}^2$

$412\text{in}^2$

$343\text{in}^2$

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. Note that all sides are equal on a cube. That is why we can use any length in the formula.

Now, we know the length of the cube is 7in.

Knowing this, we can substitute into 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 #2 : How To Find The Surface Area Of A Cube

Find the surface area of a cube with a width of 4cm.

Possible Answers:

$128\text{cm}^2$

$96\text{cm}^2$

$64\text{cm}^2$

$48\text{cm}^2$

$24\text{cm}^2$

Correct answer:

$96\text{cm}^2$

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 4in. Because it is a cube, all sides are equal (this is why we can use any length in the formula). So, we will use 4in in the formula. We get

$SA = 6 \cdot (4\text{in})^2$

$SA = 6 \cdot 16\text{in}^2$

$SA = 96\text{in}^2$

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Example Question #356 : Geometry

Find the surface area of a cube with a length of 12in.

Possible Answers:

$582\text{in}^2$

$712\text{in}^2$

$436\text{in}^2$

$864\text{in}^2$

$144\text{in}^2$

Correct answer:

$864\text{in}^2$

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 length of the cube is 12in. Because it is a cube, all lengths, widths, and heights are the same. Therefore, the width is also 12in.

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

$SA = 6 \cdot 12\text{in} \cdot 12\text{in}$

$SA = 6 \cdot 144\text{in}^2$

$SA = 864\text{in}^2$

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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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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Solid Geometry

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Surface Area Of A Cube

Example Question #353 : Geometry

Example Question #354 : Geometry

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

Example Question #356 : Geometry

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

All ISEE Upper Level Math Resources

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