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ISEE Upper Level Math : Cubes

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Example Questions

Example Question #31 : Solid Geometry

Find the volume of a cube with a height of 7in.

Possible Answers:

$349\text{in}^3$

$392\text{in}^3$

$343\text{in}^3$

$221\text{in}^3$

$147\text{in}^3$

Correct answer:

$343\text{in}^3$

Explanation:

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

$V = l \cdot w \cdot h$

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

Now, we know the height of the cube is 7in. Because it is a cube, all sides are equal. Therefore, all sides (the length, width, height) are all 7in.

So, we get

$V = 7\text{in} \cdot 7\text{in} \cdot 7\text{in}$

$V = 49\text{in}^2 \cdot 7\text{in}$

$V = 343\text{in}^3$

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

The length of the side of a cube is x -5 . Give its surface area in terms of .

Possible Answers:

$6x^{2} -60x - 150$

x^3-15 x^2-75 x+125

$6x^{2} -60x + 150$

$6x^{2} -10x + 25$

x^3-15 x^2+75 x-125

Correct answer:

$6x^{2} -60x + 150$

Explanation:

Substitute s = x - 5 in the formula for the surface area of a cube:

$A = 6s^{2}$

$A = 6 \left ( x - 5\right )^{2}$

$A = 6 \left ( x^{2} - 2 \cdot 5 \cdot x + 5^{2}\right )$

$A = 6 \left ( x^{2} - 10x +25\right )$

$A = 6 x^{2} - 60x +150$

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Example Question #31 : Solid Geometry

If a cube has one side measuring cm, what is the surface area of the cube?

Possible Answers:

Correct answer:

Explanation:

To find the surface area of a cube, use the formula $6s^{2}$ , where represents the length of the side. Since the side of the cube measures , we can substitute in for .

$6(4)^{2}=96\: cm^{2}$

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Example Question #3 : How To Find The Surface Area Of A Cube

Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5 cm, what is the surface area of the cube?

Possible Answers:

150cm^2

50cm^2

125cm^2

75cm^2

Correct answer:

150cm^2

Explanation:

Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5 cm, what is the surface area of the cube?

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

$SA_{cube}=6*s^2$

This works, because we have 6 sides, each of which has an area of s^2

Plug in our known to get our answer:

$SA_{cube}=6*(5cm)^2=6*25cm^2=150cm^2$

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Example Question #21 : Cubes

A cube has a side length of 9 mm , what is the surface area of the cube?

Possible Answers:

729mm^2

81 mm^2

486mm^2

428mm^2

Correct answer:

486mm^2

Explanation:

A cube has a side length of 9 mm , what is the surface area of the cube?

Surface area of a cube can be found as follows:

$SA_{cube}=6s^2$

Plug in our side length to find our answer:

$SA_{cube}=6(9mm)^2=6*81mm^2=486mm^2$

Making our answer:

486mm^2

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Example Question #21 : Cubes

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:

36in^2

96in^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 #22 : Cubes

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

Possible Answers:

$108\text{cm}^2$

$72\text{cm}^2$

$36\text{cm}^2$

$216\text{cm}^2$

$125\text{cm}^2$

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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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 #31 : Solid Geometry

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

Example Question #31 : Solid Geometry

Example Question #3 : How To Find The Surface Area Of A Cube

Example Question #21 : Cubes

Example Question #21 : Cubes

Example Question #22 : Cubes

Example Question #354 : Geometry

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

Example Question #356 : Geometry

All ISEE Upper Level Math Resources

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