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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

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Example Questions

Example Question #11 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Find the volume of a hemisphere with radius 341 $\displaystyle 341$. Round your answer to the nearest hundredth.

Possible Answers:

$\displaystyle 83046579.7$

$\displaystyle 166093159.41$

$\displaystyle 52869094.67$

$\displaystyle 26434547.33$

$\displaystyle 39651821$

Correct answer:

$\displaystyle 83046579.7$

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 341 for $\uptext{r}$ $\displaystyle \uptext{r}$.

$V=\frac{2}{3}\cdot\pi\cdot ( 341 )^3$ $\displaystyle V=\frac{2}{3}\cdot\pi\cdot ( 341 )^3$

$\displaystyle V= 83046579.70337164$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 83046579.7$

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Example Question #12 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

Find the volume of a hemisphere with radius $\displaystyle 7$. Round your answer to the nearest hundredth.

Possible Answers:

1436.76 $\displaystyle 1436.76$

343 $\displaystyle 343$

457.33 $\displaystyle 457.33$

228.67 $\displaystyle 228.67$

718.38 $\displaystyle 718.38$

Correct answer:

718.38 $\displaystyle 718.38$

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 $\displaystyle 7$ for $\uptext{r}$ $\displaystyle \uptext{r}$.

$V=\frac{2}{3}\cdot\pi\cdot ( 7 )^3$ $\displaystyle V=\frac{2}{3}\cdot\pi\cdot ( 7 )^3$

$\displaystyle V= 718.3775201208659$

Now we round our answer to the nearest hundredth.

$\displaystyle V= 718.38$

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

Example Question #12 : Cavalieri's Principle: Ccss.Math.Content.Hsg Gmd.A.2

All Common Core: High School - Geometry Resources

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