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 #383 : High School: Geometry

Find the volume of a cube, if its surface area is \displaystyle 897.

Round your answer to \displaystyle 2 decimal places.

Possible Answers:

\displaystyle 149.5

\displaystyle 3341362.38

\displaystyle 22350.25

\displaystyle 9.64

\displaystyle 134101.5

Correct answer:

\displaystyle 3341362.38

Explanation:

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

\displaystyle SA = 6 l

Where \displaystyle SA is surface area and \displaystyle l is the length.

Now we plug 897 for \displaystyle SA and solve for \displaystyle l.

\displaystyle \\897 = 6 l \\l = 149.5

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

\displaystyle V = w^{3}

Where \displaystyle w is the width and\displaystyle V volume.

Now plug in 149.5 for \displaystyle w.

\displaystyle \\V = \left( 149.5 \right)^{3} \\V = 3341362.375

So the final answer is.

\displaystyle 3341362.38

Example Question #384 : High School: Geometry

Find the volume of a cube, if its surface area is \displaystyle 800.

Round your answer to \displaystyle 2 decimal places.

Possible Answers:

\displaystyle 2370370.37

\displaystyle 17777.78

\displaystyle 106666.67

\displaystyle 9.28

\displaystyle 133.33

Correct answer:

\displaystyle 2370370.37

Explanation:

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

\displaystyle SA = 6 l

Where \displaystyle SA is surface area and \displaystyle l is the length.

Now we plug 800 for \displaystyle SA and solve for \displaystyle l.

\displaystyle \\800 = 6 l \\l = 133.333333333333

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

\displaystyle V = w^{3}

Where w is the width and \displaystyle V volume.

Now plug in 133.33333333333334 for \displaystyle w.

\displaystyle \\V = \left( 133.33333333333334 \right)^{3} \\V = 2370370.37037037

So the final answer is.

\displaystyle 2370370.37

Example Question #21 : Geometric Measurement & Dimension

Find the volume of a cube, if its surface area is \displaystyle 738.

Round your answer to \displaystyle 2 decimal places.

Possible Answers:

\displaystyle 90774.0

\displaystyle 15129.0

\displaystyle 9.04

\displaystyle 123.0

\displaystyle 1860867.0

Correct answer:

\displaystyle 1860867.0

Explanation:

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

\displaystyle SA = 6 l

Where \displaystyle SA is surface area and \displaystyle l is the length.

Now we plug 738 for \displaystyle SA and solve for \displaystyle l.

\displaystyle \\738 = 6 l \\l = 123.0

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

\displaystyle V = w^{3}

Where \displaystyle w is the width and \displaystyle V volume.

Now plug in 123.0 for \displaystyle w.

\displaystyle \\V = \left( 123.0 \right)^{3} \\V = 1860867.0

So the final answer is.

\displaystyle 1860867.0

 

 

Example Question #22 : 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 \displaystyle 925.

Round your answer to \displaystyle 2 decimal places.

Possible Answers:

\displaystyle 3664134.84

\displaystyle 142604.17

\displaystyle 23767.36

\displaystyle 154.17

\displaystyle 9.74

Correct answer:

\displaystyle 3664134.84

Explanation:

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

\displaystyle SA = 6 l

Where \displaystyle SA is surface area and \displaystyle l is the length.

Now we plug 925 for \displaystyle SA and solve for \displaystyle l.

\displaystyle \\925 = 6 l \\l = 154.166666666667

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

\displaystyle V = w^{3}

Where \displaystyle w is the width and \displaystyle V volume.

Now plug in 154.16666666666666 for \displaystyle w.

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

So the final answer is.

\displaystyle 3664134.84

Example Question #1 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Find the volume of a sphere with radius \displaystyle 344 . Round your answer to the nearest hundredth.

Possible Answers:

\displaystyle 85257764.56

\displaystyle 40707584

\displaystyle 170515529.12

\displaystyle 27138389.33

\displaystyle 54276778.67

Correct answer:

\displaystyle 170515529.12

Explanation:

In order to find the volume of a sphere, we need to recall the volume of a sphere equation.

\displaystyle V = \frac{4 \pi}{3} r^{3}

We simply plug in \displaystyle 344 for .

\displaystyle V=\frac{4}{3}\cdot\pi\cdot ( 344 )^3

\displaystyle V= 170515529.1197192

Now we round our answer to the nearest hundredth.


\displaystyle V= 170515529.12

Example Question #2 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Find the volume of a sphere with radius \displaystyle 399. Round your answer to the nearest hundredth.


Possible Answers:

\displaystyle 133038488.08

\displaystyle 42347466.0

\displaystyle 84694932.0

\displaystyle 266076976.17

\displaystyle 63521199

Correct answer:

\displaystyle 266076976.17

Explanation:

In order to find the volume of a sphere, we need to recall the volume of a sphere equation.

\displaystyle V = \frac{4 \pi}{3} r^{3}

We simply plug in \displaystyle 399 for .

\displaystyle V=\frac{4}{3}\cdot\pi\cdot ( 399 )^3

\displaystyle V= 266076976.16748706

Now we round our answer to the nearest hundredth.

\displaystyle V= 266076976.17



Example Question #1 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Find the volume of a sphere with radius \displaystyle 93. Round your answer to the nearest hundredth.


Possible Answers:

\displaystyle 1684641.36

\displaystyle 536238.0

\displaystyle 1072476.0

\displaystyle 3369282.72

\displaystyle 804357

Correct answer:

\displaystyle 3369282.72

Explanation:

In order to find the volume of a sphere, we need to recall the volume of a sphere equation.

\displaystyle V = \frac{4 \pi}{3} r^{3}

We simply plug in \displaystyle 93 for .

\displaystyle V=\frac{4}{3}\cdot\pi\cdot ( 93 )^3

\displaystyle V= 3369282.722751367

Now we round our answer to the nearest hundredth.


\displaystyle V= 3369282.72




Example Question #1 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Find the volume of a hemisphere with radius \displaystyle 495. Round your answer to the nearest hundredth.




Possible Answers:

\displaystyle 80858250.0

\displaystyle 508047368.36

\displaystyle 161716500.0

\displaystyle 254023684.18

\displaystyle 121287375

Correct answer:

\displaystyle 254023684.18

Explanation:

In order to find the volume of a hemisphere, we need to recall the volume of a hemisphere equation.

\displaystyle V = \frac{2 \pi}{3} r^{3}

We simply plug in \displaystyle 495 for .


\displaystyle V=\frac{2}{3}\cdot\pi\cdot ( 495 )^3

\displaystyle V= 254023684.18212688

Now we round our answer to the nearest hundredth.


\displaystyle V= 254023684.18

Example Question #21 : Geometric Measurement & Dimension

Find the volume of a sphere with radius \displaystyle 188. Round your answer to the nearest hundredth.


Possible Answers:

\displaystyle 27833136.99

\displaystyle 4429781.33

\displaystyle 13916568.49

\displaystyle 8859562.67

\displaystyle 6644672

Correct answer:

\displaystyle 27833136.99

Explanation:

In order to find the volume of a sphere, we need to recall the volume of a sphere equation.

\displaystyle V = \frac{4 \pi}{3} r^{3}

We simply plug in \displaystyle 188 for .
\displaystyle V=\frac{4}{3}\cdot\pi\cdot ( 188 )^3

\displaystyle V= 27833136.987618394

Now we round our answer to the nearest hundredth.

\displaystyle V= 27833136.99



Example Question #2 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Find the volume of a hemisphere with radius \displaystyle 347. Round your answer to the nearest hundredth.



Possible Answers:

\displaystyle 55709230.67

\displaystyle 87507854.9

\displaystyle 175015709.8

\displaystyle 41781923

\displaystyle 27854615.33

Correct answer:

\displaystyle 87507854.9

Explanation:

In order to find the volume of a hemisphere, we need to recall the volume of a hemisphere equation.

\displaystyle V = \frac{2 \pi}{3} r^{3}

We simply plug in \displaystyle 347 for .

\displaystyle V=\frac{2}{3}\cdot\pi\cdot ( 347 )^3


\displaystyle V= 87507854.8997696

Now we round our answer to the nearest hundredth.

\displaystyle V= 87507854.9



All Common Core: High School - Geometry Resources

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