Common Core: High School - Geometry : Cavalieri's Principle: CCSS.Math.Content.HSG-GMD.A.2

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

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All Common Core: High School - Geometry Resources

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Example Questions

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



Example Question #6 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Find the volume of a sphere with radius \displaystyle 224. Round your answer to the nearest hundredth.


Possible Answers:

\displaystyle 14985898.67

\displaystyle 7492949.33

\displaystyle 11239424

\displaystyle 47079589.16

\displaystyle 23539794.58

Correct answer:

\displaystyle 47079589.16

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 224 for .


\displaystyle V=\frac{4}{3}\cdot\pi\cdot ( 224 )^3

\displaystyle V= 47079589.15864107

Now we round our answer to the nearest hundredth.

\displaystyle V= 47079589.16




Example Question #7 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Find the volume of a hemisphere with radius \displaystyle 163. Round your answer to the nearest hundredth.


Possible Answers:

\displaystyle 4330747

\displaystyle 2887164.67

\displaystyle 5774329.33

\displaystyle 9070295.31

\displaystyle 18140590.61

Correct answer:

\displaystyle 9070295.31

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 163 for .

\displaystyle V=\frac{2}{3}\cdot\pi\cdot ( 163 )^3

\displaystyle V= 9070295.306504022

Now we round our answer to the nearest hundredth.

\displaystyle V= 9070295.31


Example Question #401 : High School: Geometry

Find the volume of a sphere with radius \displaystyle 409. Round your answer to the nearest hundredth.


Possible Answers:

\displaystyle 91223905.33

\displaystyle 45611952.67

\displaystyle 68417929

\displaystyle 286588350.83

\displaystyle 143294175.41

Correct answer:

\displaystyle 286588350.83

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 409 for .

\displaystyle V=\frac{4}{3}\cdot\pi\cdot ( 409 )^3

\displaystyle V= 286588350.82697076

Now we round our answer to the nearest hundredth.


\displaystyle V= 286588350.83



Example Question #401 : High School: Geometry

Find the volume of a hemisphere with radius \displaystyle 464. Round your answer to the nearest hundredth.

Possible Answers:

\displaystyle 209224508.02

\displaystyle 133196458.67

\displaystyle 99897344

\displaystyle 418449016.03

\displaystyle 66598229.33

Correct answer:

\displaystyle 209224508.02

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 464 for .

\displaystyle V=\frac{2}{3}\cdot\pi\cdot ( 464 )^3

\displaystyle V= 209224508.01568824

Now we round our answer to the nearest hundredth.

\displaystyle V= 209224508.02

All Common Core: High School - Geometry Resources

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