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ISEE Upper Level Math : Solid 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

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Example Question #16 : Cubes

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 volume of your box be?

Possible Answers:

12ft^3

18ft^3

9ft^3

27ft^3

Correct answer:

27ft^3

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 volume of your box be?

Begin with the formula for volume of a cube:

V=s^3

Where s is our side length and V is our volume.

Now, we need to plug in our side length and solve for V

V=(3ft)^3=3ft*9ft^2=27ft^3

So, our volume is

27ft^3

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Example Question #17 : Cubes

Find the volume of a cube with a width of 9in.

Possible Answers:

$549\text{in}^3$

$648\text{in}^3$

$729\text{in}^3$

$819\text{in}^3$

$436\text{in}^3$

Correct answer:

$729\text{in}^3$

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 width is 9in. Because it is a cube, all sides are equal. Therefore, the length and the height are also 9in.

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

$V = 9\text{in} \cdot9\text{in} \cdot9\text{in}$

$V = 81\text{in}^2 \cdot 9\text{in}$

$V = 729\text{in}^3$

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Example Question #18 : Cubes

Find the volume of a cube with a height of 8in.

Possible Answers:

$512\text{in}^3$

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

$336\text{in}^3$

$64\text{in}^3$

$448\text{in}^3$

Correct answer:

$512\text{in}^3$

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 8in. Because it is a cube all sides (length, height, width) are the same. So, all are 8in.

Now we can substitute. We get

$V = 8\text{in} \cdot 8\text{in} \cdot 8\text{in}$

$V = 512\text{in}^3$

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Example Question #31 : Solid Geometry

Find the volume of a cube with a length of 5in.

Possible Answers:

$125\text{in}^3$

$100\text{in}^3$

$75\text{in}^3$

$150\text{in}^3$

$175\text{in}^3$

Correct answer:

$125\text{in}^3$

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 length of the cube is 5in. Because it is a cube, all sides/lengths are equal. Therefore, the length and width are also 5in.

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

$V = 5\text{in} \cdot 5\text{in} \cdot 5\text{in}$

$V = 25\text{in}^2 \cdot 5\text{in}$

$V = 125\text{in}^3$

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Example Question #20 : Cubes

Find the volume of a cube with a height of 14cm.

Possible Answers:

$1176\text{cm}^3$

$1764\text{cm}^3$

$2548\text{cm}^3$

$2744\text{cm}^3$

$2940\text{cm}^3$

Correct answer:

$2744\text{cm}^3$

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 14cm. Because it is a cube, all sides (lengths, widths, heights) are equal. Therefore, the length and the width are also 14cm. So, we can substitute. We get

$V = 14\text{cm} \cdot14\text{cm} \cdot14\text{cm}$

$V = 14\text{cm} \cdot 196\text{cm}^2$

$V = 2744\text{cm}^2$

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Example Question #21 : Cubes

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

Possible Answers:

$221\text{in}^3$

$343\text{in}^3$

$349\text{in}^3$

$392\text{in}^3$

$147\text{in}^3$

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 : Solve For Surface Area

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

Possible Answers:

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

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

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

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

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

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 #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

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 #1 : 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:

50cm^2

150cm^2

75cm^2

125cm^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 #2 : How To Find The Surface Area Of A Cube

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

Possible Answers:

729mm^2

428mm^2

81 mm^2

486mm^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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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 #16 : Cubes

Example Question #17 : Cubes

Example Question #18 : Cubes

Example Question #31 : Solid Geometry

Example Question #20 : Cubes

Example Question #21 : Cubes

Example Question #1 : Solve For Surface Area

Example Question #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

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

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

All ISEE Upper Level Math Resources

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