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Common Core: High School - Geometry : Circumference and Area of a Circle, Volume of a Cylinder, Pyramid, and Cone Formulas: CCSS.Math.Content.HSG-GMD.A.1

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 : 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 what is the radius?

Possible Answers:

$\frac{33}{2 \pi}$

$\frac{33}{4 \pi}$

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

Correct answer:

$\frac{33}{2 \pi}$

Explanation:

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

$C = 2 \pi r$

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

$33 = 2 \pi r$

Divide by $2 \pi$ on each side to get

$r = \frac{33}{2 \pi}$

Thus the radius is

$\frac{33}{2 \pi}$

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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 and a height of what is the volume?

Possible Answers:

$50 \pi$

375

$25 \pi^{2}$

5625

$5625 \pi$

Correct answer:

$5625 \pi$

Explanation:

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

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

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

$\\r=15\rightarrow r^2=225 \\h=25$

$V = 5625 \pi$

Thus the volume is

$5625 \pi$

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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 and a height of what is the volume?

Possible Answers:

$484 \pi$

$4 \pi^{2}$

484

$8 \pi$

Correct answer:

$484 \pi$

Explanation:

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

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

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

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

$V = 484 \pi$

Thus the volume is

$484 \pi$

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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 cylinder has a radius of and a height of what is the volume?

Possible Answers:

$44 \pi$

$88 \pi$

$22 \pi^{2}$

Correct answer:

$88 \pi$

Explanation:

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

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

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

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

$V = 88 \pi$

Thus the volume is

$88 \pi$

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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 1010 and a radius of 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 cylinder.

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

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

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

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

Thus the height is

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

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Example Question #6 : 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 and a height of what is the volume?

Possible Answers:

Correct answer:

Explanation:

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

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

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

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

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

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

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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 277 and a radius of 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.

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

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

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

Thus the height is

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

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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 a base length of and a volume of 669 what is the height?

Possible Answers:

$\frac{2007}{143}$

$\frac{669}{143}$

$\frac{4028049}{20449}$

$\frac{6021}{143}$

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

Correct answer:

$\frac{2007}{143}$

Explanation:

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

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

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

w=13, l=11, V=669

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

Now we solve for .

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

Thus the height is

$\frac{2007}{143}$

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Example Question #9 : 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 837 and a radius of what is the height?

Possible Answers:

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

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

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

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

$\frac{837}{4}$

Correct answer:

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

Explanation:

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

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

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

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

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

Thus the height is

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

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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 909 and a radius of 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 cylinder.

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

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

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

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

Thus the height is

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

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All Common Core: High School - Geometry Resources

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Common Core: High School - Geometry : Circumference and Area of a Circle, Volume of a Cylinder, Pyramid, and Cone Formulas: CCSS.Math.Content.HSG-GMD.A.1

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

All Common Core: High School - Geometry Resources

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

Example Question #2 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #3 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #4 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #2 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #6 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #7 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #8 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #9 : Circumference And Area Of A Circle, Volume Of A Cylinder, Pyramid, And Cone Formulas: Ccss.Math.Content.Hsg Gmd.A.1

Example Question #10 : 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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