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Common Core: High School - Geometry : Geometric Measurement & Dimension

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

If a cylinder has a volume of 1586 and a radius of what is the height?

Possible Answers:

$\frac{793}{72}$

$\frac{793}{72 \pi}$

$\frac{793}{36 \pi}$

$\frac{628849}{5184 \pi^{2}}$

$\frac{793}{144 \pi}$

Correct answer:

$\frac{793}{72 \pi}$

Explanation:

In order to find the height, we need to recall the equation for the volume of a cylinder.

$V = \pi h r^{2}$

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\\1586 = 144 \pi h \\\\h = \frac{793}{72 \pi}$

Thus the height is

$\frac{793}{72 \pi}$

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Example Question #12 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

If a cone has a volume of 1928 and a radius of what is the height?

Possible Answers:

Correct answer:

Explanation:

In order to find the height, we need to recall the equation for the volume of a cone.

$V = \frac{\pi h}{3} r^{2}$

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\\ 1928 = 3 \pi h \\\\h = \frac{1928}{3 \pi}$

Thus the height is

$\frac{1928}{3 \pi}$

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Example Question #13 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Find the volume of a cube, if its surface area is 539 .

Round your answer to decimal places.

Possible Answers:

8070.03

724957.5

8.14

48420.17

89.83

Correct answer:

724957.5

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

SA = 6 l

Where is surface area and l is the length.

Now we plug 539 for and solve for .

$\\539 = 6 l \\l = 89.8333333333333$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where w is the width and V volume.

Now plug in 89.83333333333333 for .

$\\V = \left( 89.83333333333333 \right)^{3} \\V = 724957.49537037$

So the final answer is.

724957.5

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Example Question #14 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Find the volume of a cube, if its surface area is 715 .

Round your answer to decimal places.

Possible Answers:

8.94

1692249.42

14200.69

119.17

85204.17

Correct answer:

1692249.42

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

SA = 6 l

Where is surface area and is the length.

Now we plug 715 for and solve for .

$\\715 = 6 l \\l = 119.166666666667$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 119.16666666666667 for .

$\\V = \left( 119.16666666666667 \right)^{3} \\V = 1692249.4212963$

So the final answer is.

1692249.42

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Example Question #15 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Find the volume of a cube, if its surface area is 925 .

Round your answer to decimal places.

Possible Answers:

23767.36

142604.17

154.17

9.74

3664134.84

Correct answer:

3664134.84

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

SA = 6 l

Where is surface area and is the length.

Now we plug 925 for and solve for .

$\\925 = 6 l \\l = 154.166666666667$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where w is the width and volume.

Now plug in 154.16666666666666 for .

$\\V = \left( 154.16666666666666 \right)^{3} \\V = 3664134.83796296$

So the final answer is.

3664134.84

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Example Question #15 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Find the volume of a cube, if its surface area is 729 .

Round your answer to decimal places.

Possible Answers:

1793613.38

9.0

121.5

14762.25

88573.5

Correct answer:

1793613.38

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

SA = 6 l

Where is surface area and is the length.

Now we plug 729 for and solve for .

$\\729 = 6 l \\l = 121.5$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 121.5 for .

$\\V = \left( 121.5 \right)^{3} \\V = 1793613.375$

So the final answer is.

1793613.38

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Example Question #16 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Find the volume of a cube, if its surface area is 584 .

Round your answer to decimal places.

Possible Answers:

97.33

922114.37

8.36

56842.67

9473.78

Correct answer:

922114.37

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

SA = 6 l

Where is surface area and is the length.

Now we plug 584 for and solve for .

$\\584 = 6 l \\l = 97.3333333333333$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 97.33333333333333 for .

$\\V = \left( 97.33333333333333 \right)^{3} \\V = 922114.37037037$

So the final answer is.

922114.37

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Example Question #16 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Find the volume of a cube, if its surface area is 744 .

Round your answer to decimal places.

Possible Answers:

92256.0

1906624.0

9.06

15376.0

9.06

124.0

15376.0

92256.0

1906624.0

Correct answer:

1906624.0

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

SA = 6 l

Where is surface area and is the length.

Now we plug 744 for and solve for .

$\\744 = 6 l \\l = 124.0$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 124.0 for .

$\\V = \left( 124.0 \right)^{3} \\V = 1906624.0$

So the final answer is.

1906624.0

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Example Question #17 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Find the volume of a cube, if its surface area is 511 .

Round your answer to decimal places.

Possible Answers:

7.99

85.17

617744.59

7253.36

43520.17

Correct answer:

617744.59

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

SA = 6 l

Where is surface area and is the length.

Now we plug 511 for and solve for .

$\\511 = 6 l \\l = 85.1666666666667$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where w is the width and V volume.

Now plug in 85.16666666666667 for .

$\\V = \left( 85.16666666666667 \right)^{3} \\V = 617744.587962963$

So the final answer is.

617744.59

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Example Question #18 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Find the volume of a cube, if its surface area is 520 .

Round your answer to decimal places.

Possible Answers:

45066.67

86.67

7511.11

650962.96

8.04

Correct answer:

650962.96

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

SA = 6 l

Where is surface area and is the length.

Now we plug 520 for and solve for .

$\\520 = 6 l \\l = 86.6666666666667$

Now since we have the width, we can plug it into the volume formula, which is

$V = w^{3}$

Where is the width and volume.

Now plug in 86.66666666666667 for .

$\\V = \left( 86.66666666666667 \right)^{3} \\V = 650962.962962963$

So the final answer is.

650962.96

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

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Common Core: High School - Geometry : Geometric Measurement & Dimension

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #11 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #12 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #13 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #14 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #15 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #15 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #16 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #16 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #17 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #18 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

All Common Core: High School - Geometry Resources

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