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

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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 344 $\displaystyle 344$ . Round your answer to the nearest hundredth.

Possible Answers:

$\displaystyle 85257764.56$

$\displaystyle 27138389.33$

$\displaystyle 54276778.67$

$\displaystyle 170515529.12$

$\displaystyle 40707584$

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.

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

We simply plug in 344 $\displaystyle 344$ for $\uptext{r}$ $\displaystyle \uptext{r}$.

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

$\displaystyle V= 170515529.1197192$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 170515529.12$

Report an Error

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

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

Possible Answers:

$\displaystyle 84694932.0$

$\displaystyle 133038488.08$

$\displaystyle 63521199$

$\displaystyle 266076976.17$

$\displaystyle 42347466.0$

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.

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

We simply plug in 399 $\displaystyle 399$ for $\uptext{r}$ $\displaystyle \uptext{r}$.

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

$\displaystyle V= 266076976.16748706$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 266076976.17$

Report an Error

Example Question #3 : 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:

$\displaystyle 1684641.36$

$\displaystyle 1072476.0$

$\displaystyle 536238.0$

$\displaystyle 3369282.72$

804357 $\displaystyle 804357$

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.

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

We simply plug in $\displaystyle 93$ for $\uptext{r}$ $\displaystyle \uptext{r}$.

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

$\displaystyle V= 3369282.722751367$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 3369282.72$

Report an Error

Example Question #4 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

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

Possible Answers:

$\displaystyle 121287375$

$\displaystyle 254023684.18$

$\displaystyle 508047368.36$

$\displaystyle 161716500.0$

$\displaystyle 80858250.0$

Correct answer:

$\displaystyle 254023684.18$

Explanation:

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

$\displaystyle V= 254023684.18212688$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 254023684.18$

Report an Error

Example Question #5 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

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

Possible Answers:

$\displaystyle 13916568.49$

6644672 $\displaystyle 6644672$

$\displaystyle 27833136.99$

$\displaystyle 4429781.33$

$\displaystyle 8859562.67$

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.

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

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

$\displaystyle V= 27833136.987618394$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 27833136.99$

Report an Error

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

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

Possible Answers:

$\displaystyle 41781923$

$\displaystyle 87507854.9$

$\displaystyle 55709230.67$

$\displaystyle 175015709.8$

$\displaystyle 27854615.33$

Correct answer:

$\displaystyle 87507854.9$

Explanation:

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

$\displaystyle V= 87507854.8997696$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 87507854.9$

Report an Error

Example Question #31 : Geometric Measurement & Dimension

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

Possible Answers:

$\displaystyle 23539794.58$

$\displaystyle 7492949.33$

$\displaystyle 11239424$

$\displaystyle 14985898.67$

$\displaystyle 47079589.16$

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.

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

We simply plug in 224 $\displaystyle 224$ for $\uptext{r}$ $\displaystyle \uptext{r}$.

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

$\displaystyle V= 47079589.15864107$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 47079589.16$

Report an Error

Example Question #32 : Geometric Measurement & Dimension

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

Possible Answers:

$\displaystyle 18140590.61$

$\displaystyle 9070295.31$

4330747 $\displaystyle 4330747$

$\displaystyle 2887164.67$

$\displaystyle 5774329.33$

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.

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

We simply plug in 163 $\displaystyle 163$ for $\uptext{r}$ $\displaystyle \uptext{r}$.

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

$\displaystyle V= 9070295.306504022$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 9070295.31$

Report an Error

Example Question #33 : Geometric Measurement & Dimension

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

Possible Answers:

$\displaystyle 68417929$

$\displaystyle 45611952.67$

$\displaystyle 286588350.83$

$\displaystyle 143294175.41$

$\displaystyle 91223905.33$

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.

$V = \frac{4 \pi}{3} r^{3}$ $\displaystyle V = \frac{4 \pi}{3} r^{3}$
We simply plug in 409 $\displaystyle 409$ for $\uptext{r}$ $\displaystyle \uptext{r}$.

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

$\displaystyle V= 286588350.82697076$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 286588350.83$

Report an Error

Example Question #34 : Geometric Measurement & Dimension

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

Possible Answers:

$\displaystyle 99897344$

$\displaystyle 133196458.67$

$\displaystyle 66598229.33$

$\displaystyle 418449016.03$

$\displaystyle 209224508.02$

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.

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

We simply plug in 464 $\displaystyle 464$ for $\uptext{r}$ $\displaystyle \uptext{r}$.

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

$\displaystyle V= 209224508.01568824$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 209224508.02$

Report an Error

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All Common Core: High School - Geometry Resources

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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

All Common Core: High School - Geometry Resources

Example Questions

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

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

Example Question #3 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Example Question #4 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Example Question #5 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

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

Example Question #31 : Geometric Measurement & Dimension

Example Question #32 : Geometric Measurement & Dimension

Example Question #33 : Geometric Measurement & Dimension

Example Question #34 : Geometric Measurement & Dimension

All Common Core: High School - Geometry Resources

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