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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

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Example Questions

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.

$\displaystyle V= 47079589.16$

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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.

$\displaystyle V= 9070295.31$

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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.

$\displaystyle V= 286588350.83$

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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.

$\displaystyle V= 209224508.02$

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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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Example Question #401 : High School: Geometry

Find the volume of a sphere, where the radius is $\displaystyle 8$.

Possible Answers:

V = 512 $\displaystyle V = 512$

$V = \frac{2048}{3}$ $\displaystyle V = \frac{2048}{3}$

$V = \frac{2048 \pi}{3}$ $\displaystyle V = \frac{2048 \pi}{3}$

$V = \frac{256 \pi}{3}$ $\displaystyle V = \frac{256 \pi}{3}$

$V = 512 \pi$ $\displaystyle V = 512 \pi$

Correct answer:

$V = \frac{2048 \pi}{3}$ $\displaystyle V = \frac{2048 \pi}{3}$

Explanation:

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

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

Since we are given the radius ( $\uptext{r}$ $\displaystyle \uptext{r}$), we can plug it into the equation.

$V = \frac{2048 \pi}{3}$ $\displaystyle V = \frac{2048 \pi}{3}$

Thus the volume is, $\frac{2048 \pi}{3}$ $\displaystyle \frac{2048 \pi}{3}$

Here is a picture representation of the sphere.

Plot1

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Example Question #1 : Cylinders, Pyramids, Cones, And Spheres Volume Formulas: Ccss.Math.Content.Hsg Gmd.A.3

Find the volume of a sphere, where the radius is $\displaystyle 9$.

Possible Answers:

$V = 108 \pi$ $\displaystyle V = 108 \pi$

V = 972 $\displaystyle V = 972$

$V = 729 \pi$ $\displaystyle V = 729 \pi$

V = 729 $\displaystyle V = 729$

$V = 972 \pi$ $\displaystyle V = 972 \pi$

Correct answer:

$V = 972 \pi$ $\displaystyle V = 972 \pi$

Explanation:

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

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

Since we are given the radius ( $\uptext{r}$ $\displaystyle \uptext{r}$), we can plug it into the equation.

$V = 972 \pi$ $\displaystyle V = 972 \pi$

Thus the volume is, $972 \pi$ $\displaystyle 972 \pi$

Here is a picture representation of the sphere.

Plot2

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Example Question #37 : Geometric Measurement & Dimension

Find the volume of a sphere, where the radius is $\displaystyle 24$.

Possible Answers:

$\displaystyle V = 18432$

$V = 13824 \pi$ $\displaystyle V = 13824 \pi$

$V = 18432 \pi$ $\displaystyle V = 18432 \pi$

$\displaystyle V = 13824$

$V = 768 \pi$ $\displaystyle V = 768 \pi$

Correct answer:

$V = 18432 \pi$ $\displaystyle V = 18432 \pi$

Explanation:

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

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

Since we are given the radius ( $\uptext{r}$ $\displaystyle \uptext{r}$), we can plug it into the equation.

$V = 18432 \pi$ $\displaystyle V = 18432 \pi$

Thus the volume is, $18432 \pi$ $\displaystyle 18432 \pi$

Here is a picture representation of the sphere.

Plot6

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Example Question #38 : Geometric Measurement & Dimension

Find the volume of a sphere, where the radius is $\displaystyle 23$.

Possible Answers:

$V = \frac{2116 \pi}{3}$ $\displaystyle V = \frac{2116 \pi}{3}$

$V = \frac{48668 \pi}{3}$ $\displaystyle V = \frac{48668 \pi}{3}$

$\displaystyle V = 12167$

$V = \frac{48668}{3}$ $\displaystyle V = \frac{48668}{3}$

$V = 12167 \pi$ $\displaystyle V = 12167 \pi$

Correct answer:

$V = \frac{48668 \pi}{3}$ $\displaystyle V = \frac{48668 \pi}{3}$

Explanation:

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

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

Since we are given the radius ( $\uptext{r}$ $\displaystyle \uptext{r}$), we can plug it into the equation.

$V = \frac{48668 \pi}{3}$ $\displaystyle V = \frac{48668 \pi}{3}$

Thus the volume is, $\frac{48668 \pi}{3}$ $\displaystyle \frac{48668 \pi}{3}$

Here is a picture representation of the sphere.

Plot12

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All Common Core: High School - Geometry Resources

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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 #31 : Geometric Measurement & Dimension

Example Question #32 : Geometric Measurement & Dimension

Example Question #33 : Geometric Measurement & Dimension

Example Question #34 : Geometric Measurement & Dimension

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

Example Question #401 : High School: Geometry

Example Question #1 : Cylinders, Pyramids, Cones, And Spheres Volume Formulas: Ccss.Math.Content.Hsg Gmd.A.3

Example Question #37 : Geometric Measurement & Dimension

Example Question #38 : Geometric Measurement & Dimension

All Common Core: High School - Geometry Resources

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