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

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

Possible Answers:

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

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

\displaystyle 2

\displaystyle 33

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

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 #1 : Geometric Measurement & Dimension

If a cylinder has a radius of \displaystyle 15 and a height of \displaystyle 25 what is the volume?

Possible Answers:

\displaystyle 375

\displaystyle 25 \pi^{2}

\displaystyle 5625

\displaystyle 50 \pi

\displaystyle 5625 \pi

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 484 \pi

\displaystyle 4 \pi^{2}

\displaystyle 484

\displaystyle 8 \pi

\displaystyle 44

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 #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 2 and a height of \displaystyle 22 what is the volume?

Possible Answers:

\displaystyle 22 \pi^{2}

\displaystyle 44

\displaystyle 44 \pi

\displaystyle 88 \pi

\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 #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 volume of \displaystyle 1010 and a radius of \displaystyle 13 what is the height?

Possible Answers:
\(\displaystyle \frac{1010}{169 \pi}\)

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

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

\(\displaystyle \frac{1010}{169}\)
\(\displaystyle \frac{1020100}{28561 \pi^{2}}\)
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 #4 : 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 radius of \displaystyle 8 and a height of \displaystyle 11 what is the volume?

Possible Answers:
\(\displaystyle \frac{704 \pi}{3}\)
\(\displaystyle 11 \pi^{2}\)

\displaystyle 88

\(\displaystyle 704\)
\(\displaystyle 22 \pi\)
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 #7 : 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 \displaystyle 277 and a radius of \displaystyle 3 what is the height?

Possible Answers:
\(\displaystyle \frac{277}{3}\)
\(\displaystyle \frac{554}{3 \pi}\)
\(\displaystyle \frac{277}{3 \pi}\)
\(\displaystyle \frac{76729}{9 \pi^{2}}\)
\(\displaystyle \frac{277}{6 \pi}\)
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 #8 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

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{2007}{143}

\displaystyle \frac{669}{143}

\displaystyle \frac{4028049}{20449}

\displaystyle \frac{6021}{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 #5 : 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{700569}{16 \pi^{2}}

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

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

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

\displaystyle \frac{837}{4}

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 #10 : 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:
\(\displaystyle \frac{909}{100 \pi}\)
\(\displaystyle \frac{826281}{10000 \pi^{2}}\)
\(\displaystyle \frac{909}{200 \pi}\)
\(\displaystyle \frac{909}{100}\)
\(\displaystyle \frac{909}{50 \pi}\)
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.

\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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