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 #1 : Geometric Measurement & Dimension

If a circle has a circumference of \(\displaystyle 33\) what is the radius?

Possible Answers:

\(\displaystyle \frac{33}{2 \pi}\)

\(\displaystyle \frac{33}{4 \pi}\)

\(\displaystyle \frac{1089}{4 \pi^{2}}\)

\(\displaystyle 33\)

\(\displaystyle 2\)

Correct answer:

\(\displaystyle \frac{33}{2 \pi}\)

Explanation:

In order to find the radius of a circle, we need to recall the equation that involves both the radius and circumference.

\(\displaystyle C = 2 \pi r\)

Since we are given the circumference, we simply substitute 33 for \(\displaystyle \uptext{C}\), and solve for \(\displaystyle \uptext{r}\).

\(\displaystyle 33 = 2 \pi r\)

Divide by \(\displaystyle 2 \pi\) on each side to get

\(\displaystyle r = \frac{33}{2 \pi}\)

Thus the radius is

\(\displaystyle \frac{33}{2 \pi}\)

Example Question #2 : 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 radius of \(\displaystyle 15\) and a height of \(\displaystyle 25\) what is the volume?

Possible Answers:

\(\displaystyle 50 \pi\)

\(\displaystyle 25 \pi^{2}\)

\(\displaystyle 5625 \pi\)

\(\displaystyle 5625\)

\(\displaystyle 375\)

Correct answer:

\(\displaystyle 5625 \pi\)

Explanation:

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

\(\displaystyle V = \pi h r^{2}\)

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

\(\displaystyle \\r=15\rightarrow r^2=225 \\h=25\)

 

\(\displaystyle V = 5625 \pi\)

Thus the volume is

\(\displaystyle 5625 \pi\)

Example Question #3 : 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 radius of \(\displaystyle 11\) and a height of \(\displaystyle 4\) what is the volume?

Possible Answers:

\(\displaystyle 44\)

\(\displaystyle 484\)

\(\displaystyle 8 \pi\)

\(\displaystyle 4 \pi^{2}\)

\(\displaystyle 484 \pi\)

Correct answer:

\(\displaystyle 484 \pi\)

Explanation:

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

\(\displaystyle V = \pi h r^{2}\)

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

\(\displaystyle \\r=11\rightarrow r^2=121 \\h=4\)

\(\displaystyle V = 484 \pi\)

Thus the volume is

\(\displaystyle 484 \pi\)

 

Example Question #1 : Geometric Measurement & Dimension

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

Possible Answers:

\(\displaystyle 88 \pi\)

\(\displaystyle 44 \pi\)

\(\displaystyle 22 \pi^{2}\)

\(\displaystyle 44\)

\(\displaystyle 88\)

Correct answer:

\(\displaystyle 88 \pi\)

Explanation:

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

\(\displaystyle V = \pi h r^{2}\)

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

\(\displaystyle \\r=2\rightarrow r^2=4 \\h=22\)

\(\displaystyle V = 88 \pi\)

Thus the volume is

\(\displaystyle 88 \pi\)

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 \(\displaystyle 1010\) and a radius of \(\displaystyle 13\) what is the height?

Possible Answers:
\(\displaystyle \frac{2020}{169 \pi}\)

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

\(\displaystyle \frac{1020100}{28561 \pi^{2}}\)
\(\displaystyle \frac{505}{169 \pi}\)

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

\(\displaystyle V = \pi h r^{2}\)

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

\(\displaystyle \\V=1010 \\r=13\)

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

Thus the height is

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

Example Question #2 : Geometric Measurement & Dimension

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

Possible Answers:

\(\displaystyle 88\)

\(\displaystyle 704\)
\(\displaystyle \frac{704 \pi}{3}\)
\(\displaystyle 11 \pi^{2}\)
\(\displaystyle 22 \pi\)
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.

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

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

\(\displaystyle \\r=8 \\h=11\)

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

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

Example Question #371 : High School: Geometry

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

Possible Answers:
\(\displaystyle \frac{277}{3}\)
\(\displaystyle \frac{277}{6 \pi}\)
\(\displaystyle \frac{277}{3 \pi}\)
\(\displaystyle \frac{76729}{9 \pi^{2}}\)
\(\displaystyle \frac{554}{3 \pi}\)
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.

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

\(\displaystyle \\V=277 \\r=3\)

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

Thus the height is

\(\displaystyle \frac{277}{3 \pi}\) 

Example Question #372 : High School: Geometry

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

Possible Answers:

\(\displaystyle \frac{6021}{143}\)

\(\displaystyle \frac{2007}{143}\)

\(\displaystyle \frac{4028049}{20449}\)

\(\displaystyle \frac{669}{143}\)

\(\displaystyle \frac{2007 \pi}{143}\)

Correct answer:

\(\displaystyle \frac{2007}{143}\)

Explanation:

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

\(\displaystyle V = \frac{h lw}{3}\)

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

\(\displaystyle w=13, l=11, V=669\)

\(\displaystyle 669 = \frac{143 h}{3}\)

Now we solve for \(\displaystyle h\).

\(\displaystyle h = \frac{2007}{143}\)

Thus the height is

\(\displaystyle \frac{2007}{143}\)

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 \(\displaystyle 837\) and a radius of \(\displaystyle 2\) what is the height?

Possible Answers:

\(\displaystyle \frac{837}{2 \pi}\)

\(\displaystyle \frac{700569}{16 \pi^{2}}\)

\(\displaystyle \frac{837}{4}\)

\(\displaystyle \frac{837}{4 \pi}\)

\(\displaystyle \frac{837}{8 \pi}\)

Correct answer:

\(\displaystyle \frac{837}{4 \pi}\)

Explanation:

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

\(\displaystyle V = \pi h r^{2}\)

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

\(\displaystyle \\V=837 \\r=2\)

\(\displaystyle 837 = 4 \pi h = \frac{837}{4 \pi}\)

Thus the height is

\(\displaystyle \frac{837}{4 \pi}\) 

Example Question #2 : 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 \(\displaystyle 909\) and a radius of \(\displaystyle 10\) what is the height?

Possible Answers:
\(\displaystyle \frac{826281}{10000 \pi^{2}}\)
\(\displaystyle \frac{909}{50 \pi}\)
\(\displaystyle \frac{909}{200 \pi}\)
\(\displaystyle \frac{909}{100 \pi}\)
\(\displaystyle \frac{909}{100}\)
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.

\(\displaystyle V = \pi h r^{2}\)

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

\(\displaystyle \\V=909 \\r=10\)

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

Thus the height is

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

All Common Core: High School - Geometry Resources

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