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Common Core: High School - Geometry : High School: Geometry

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 #3 : Geometric Measurement & Dimension

If a cylinder has a radius of $\displaystyle 11$ and a height of $\displaystyle 4$ what is the volume?

Possible Answers:

$8 \pi$ $\displaystyle 8 \pi$

$\displaystyle 44$

484 $\displaystyle 484$

$484 \pi$ $\displaystyle 484 \pi$

$4 \pi^{2}$ $\displaystyle 4 \pi^{2}$

Correct answer:

$484 \pi$ $\displaystyle 484 \pi$

Explanation:

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

$V = \pi h r^{2}$ $\displaystyle V = \pi h r^{2}$

Since we are given the radius, and the height, we can simply plug in those values into the equation.

$\\r=11\rightarrow r^2=121 \\h=4$ $\displaystyle \\r=11\rightarrow r^2=121 \\h=4$

$V = 484 \pi$ $\displaystyle V = 484 \pi$

Thus the volume is

$484 \pi$ $\displaystyle 484 \pi$

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Example Question #2 : Geometric Measurement & Dimension

If a cylinder has a radius of $\displaystyle 2$ and a height of $\displaystyle 22$ what is the volume?

Possible Answers:

$44 \pi$ $\displaystyle 44 \pi$

$\displaystyle 44$

$88 \pi$ $\displaystyle 88 \pi$

$22 \pi^{2}$ $\displaystyle 22 \pi^{2}$

$\displaystyle 88$

Correct answer:

$88 \pi$ $\displaystyle 88 \pi$

Explanation:

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

$V = \pi h r^{2}$ $\displaystyle V = \pi h r^{2}$

Since we are given the radius, and the height, we can simply plug in those values into the equation.

$\\r=2\rightarrow r^2=4 \\h=22$ $\displaystyle \\r=2\rightarrow r^2=4 \\h=22$

$V = 88 \pi$ $\displaystyle V = 88 \pi$

Thus the volume is

$88 \pi$ $\displaystyle 88 \pi$

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Example Question #1 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

If a cylinder has a volume of 1010 $\displaystyle 1010$ and a radius of $\displaystyle 13$ what is the height?

Possible Answers:

\(\displaystyle \frac{1020100}{28561 \pi^{2}}\)

\(\displaystyle \frac{1010}{169 \pi}\)

\(\displaystyle \frac{2020}{169 \pi}\)

\(\displaystyle \frac{1010}{169}\)

\(\displaystyle \frac{505}{169 \pi}\)

Correct answer:

\(\displaystyle \frac{1010}{169 \pi}\)

Explanation:

In order to find the height, we need to recall the equation for the volume of a cylinder.

$V = \pi h r^{2}$ $\displaystyle V = \pi h r^{2}$

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\\V=1010 \\r=13$ $\displaystyle \\V=1010 \\r=13$

$\\1010 = 169 \pi h \\\\h = \frac{1010}{169 \pi}$ $\displaystyle \\1010 = 169 \pi h \\\\h = \frac{1010}{169 \pi}$

Thus the height is

$\frac{1010}{169 \pi}$ $\displaystyle \frac{1010}{169 \pi}$

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Example Question #3 : Geometric Measurement & Dimension

If a cone has a radius of $\displaystyle 8$ and a height of $\displaystyle 11$ what is the volume?

Possible Answers:

\(\displaystyle 11 \pi^{2}\)

\(\displaystyle 22 \pi\)

$\displaystyle 88$

\(\displaystyle 704\)

\(\displaystyle \frac{704 \pi}{3}\)

Correct answer:

\(\displaystyle \frac{704 \pi}{3}\)

Explanation:

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

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

Since we are given the radius, and the height, we can simply plug in those values into the equation.

$\\r=8 \\h=11$ $\displaystyle \\r=8 \\h=11$

$V = \frac{704 \pi}{3}$ $\displaystyle V = \frac{704 \pi}{3}$
Thus the volume is

$\frac{704 \pi}{3}$ $\displaystyle \frac{704 \pi}{3}$

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Example Question #7 : Geometric Measurement & Dimension

If a cone has a volume of 277 $\displaystyle 277$ and a radius of $\displaystyle 3$ what is the height?

Possible Answers:

\(\displaystyle \frac{277}{3}\)

\(\displaystyle \frac{76729}{9 \pi^{2}}\)

\(\displaystyle \frac{554}{3 \pi}\)

\(\displaystyle \frac{277}{6 \pi}\)

\(\displaystyle \frac{277}{3 \pi}\)

Correct answer:

\(\displaystyle \frac{277}{3 \pi}\)

Explanation:

In order to find the height, we need to recall the equation for the volume of a cone.

$V = \frac{\pi h}{3} r^{2}$ $\displaystyle V = \frac{\pi h}{3} r^{2}$
Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\\V=277 \\r=3$ $\displaystyle \\V=277 \\r=3$

$\\277 = 3 \pi h \\\\h = \frac{277}{3 \pi}$ $\displaystyle \\277 = 3 \pi h \\\\h = \frac{277}{3 \pi}$

Thus the height is

$\frac{277}{3 \pi}$ $\displaystyle \frac{277}{3 \pi}$

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Example Question #8 : Geometric Measurement & Dimension

If a pyramid has a base width of $\displaystyle 13$ a base length of $\displaystyle 11$ and a volume of 669 $\displaystyle 669$ what is the height?

Possible Answers:

$\frac{2007}{143}$ $\displaystyle \frac{2007}{143}$

$\frac{2007 \pi}{143}$ $\displaystyle \frac{2007 \pi}{143}$

$\frac{669}{143}$ $\displaystyle \frac{669}{143}$

$\frac{6021}{143}$ $\displaystyle \frac{6021}{143}$

$\frac{4028049}{20449}$ $\displaystyle \frac{4028049}{20449}$

Correct answer:

$\frac{2007}{143}$ $\displaystyle \frac{2007}{143}$

Explanation:

In order to find the height, we need to recall the equation for the volume of a pyramid,

$V = \frac{h lw}{3}$ $\displaystyle V = \frac{h lw}{3}$

Since we are given the length, width, and volume, we can simply plug those values into the equation.

$\displaystyle w=13, l=11, V=669$

$669 = \frac{143 h}{3}$ $\displaystyle 669 = \frac{143 h}{3}$

Now we solve for $\displaystyle h$ .

$h = \frac{2007}{143}$ $\displaystyle h = \frac{2007}{143}$

Thus the height is

$\frac{2007}{143}$ $\displaystyle \frac{2007}{143}$

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Example Question #9 : Geometric Measurement & Dimension

If a cylinder has a volume of 837 $\displaystyle 837$ and a radius of $\displaystyle 2$ what is the height?

Possible Answers:

$\frac{837}{8 \pi}$ $\displaystyle \frac{837}{8 \pi}$

$\frac{700569}{16 \pi^{2}}$ $\displaystyle \frac{700569}{16 \pi^{2}}$

$\frac{837}{4 \pi}$ $\displaystyle \frac{837}{4 \pi}$

$\frac{837}{4}$ $\displaystyle \frac{837}{4}$

$\frac{837}{2 \pi}$ $\displaystyle \frac{837}{2 \pi}$

Correct answer:

$\frac{837}{4 \pi}$ $\displaystyle \frac{837}{4 \pi}$

Explanation:

In order to find the height, we need to recall the equation for the volume of a cylinder.

$V = \pi h r^{2}$ $\displaystyle V = \pi h r^{2}$

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\\V=837 \\r=2$ $\displaystyle \\V=837 \\r=2$

$837 = 4 \pi h = \frac{837}{4 \pi}$ $\displaystyle 837 = 4 \pi h = \frac{837}{4 \pi}$

Thus the height is

$\frac{837}{4 \pi}$ $\displaystyle \frac{837}{4 \pi}$

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Example Question #1 : Geometric Measurement & Dimension

If a cylinder has a volume of 909 $\displaystyle 909$ and a radius of $\displaystyle 10$ what is the height?

Possible Answers:

\(\displaystyle \frac{909}{100}\)

\(\displaystyle \frac{909}{200 \pi}\)

\(\displaystyle \frac{826281}{10000 \pi^{2}}\)

\(\displaystyle \frac{909}{100 \pi}\)

\(\displaystyle \frac{909}{50 \pi}\)

Correct answer:

\(\displaystyle \frac{909}{100 \pi}\)

Explanation:

In order to find the height, we need to recall the equation for the volume of a cylinder.

$V = \pi h r^{2}$ $\displaystyle V = \pi h r^{2}$

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\\V=909 \\r=10$ $\displaystyle \\V=909 \\r=10$

$\\909 = 100 \pi h \\\\h = \frac{909}{100 \pi}$ $\displaystyle \\909 = 100 \pi h \\\\h = \frac{909}{100 \pi}$

Thus the height is

$\frac{909}{100 \pi}$ $\displaystyle \frac{909}{100 \pi}$

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Example Question #11 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

If a cylinder has a volume of 1586 $\displaystyle 1586$ and a radius of $\displaystyle 12$ what is the height?

Possible Answers:

$\frac{793}{144 \pi}$ $\displaystyle \frac{793}{144 \pi}$

$\frac{793}{36 \pi}$ $\displaystyle \frac{793}{36 \pi}$

$\frac{628849}{5184 \pi^{2}}$ $\displaystyle \frac{628849}{5184 \pi^{2}}$

$\frac{793}{72}$ $\displaystyle \frac{793}{72}$

$\frac{793}{72 \pi}$ $\displaystyle \frac{793}{72 \pi}$

Correct answer:

$\frac{793}{72 \pi}$ $\displaystyle \frac{793}{72 \pi}$

Explanation:

In order to find the height, we need to recall the equation for the volume of a cylinder.

$V = \pi h r^{2}$ $\displaystyle V = \pi h r^{2}$

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\\1586 = 144 \pi h \\\\h = \frac{793}{72 \pi}$ $\displaystyle \\1586 = 144 \pi h \\\\h = \frac{793}{72 \pi}$

Thus the height is

$\frac{793}{72 \pi}$ $\displaystyle \frac{793}{72 \pi}$

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Example Question #12 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

If a cone has a volume of 1928 $\displaystyle 1928$ and a radius of $\displaystyle 3$ what is the height?

Possible Answers:

Correct answer:

Explanation:

In order to find the height, we need to recall the equation for the volume of a cone.

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

Since we are given the volume, and the radius, we can simply plug in those values into the equation.

$\\ 1928 = 3 \pi h \\\\h = \frac{1928}{3 \pi}$ $\displaystyle \\ 1928 = 3 \pi h \\\\h = \frac{1928}{3 \pi}$

Thus the height is

$\frac{1928}{3 \pi}$ $\displaystyle \frac{1928}{3 \pi}$

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All Common Core: High School - Geometry Resources

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Common Core: High School - Geometry : High School: Geometry

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

All Common Core: High School - Geometry Resources

Example Questions

Example Question #3 : Geometric Measurement & Dimension

Example Question #2 : Geometric Measurement & Dimension

Example Question #1 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #3 : Geometric Measurement & Dimension

Example Question #7 : Geometric Measurement & Dimension

Example Question #8 : Geometric Measurement & Dimension

Example Question #9 : Geometric Measurement & Dimension

Example Question #1 : Geometric Measurement & Dimension

Example Question #11 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #12 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

All Common Core: High School - Geometry Resources

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