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Common Core: High School - Geometry : Cylinders, Pyramids, Cones, and Spheres Volume Formulas: CCSS.Math.Content.HSG-GMD.A.3

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Example Questions

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 .

Possible Answers:

V = 512

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

$V = 512 \pi$

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

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

Correct answer:

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

Explanation:

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

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

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

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

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

Here is a picture representation of the sphere.

Plot1

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Example Question #2 : Cylinders, Pyramids, Cones, And Spheres Volume Formulas: Ccss.Math.Content.Hsg Gmd.A.3

Find the volume of a sphere, where the radius is .

Possible Answers:

$V = 108 \pi$

V = 972

V = 729

$V = 729 \pi$

$V = 972 \pi$

Correct answer:

$V = 972 \pi$

Explanation:

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

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

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

$V = 972 \pi$

Thus the volume is, $972 \pi$

Here is a picture representation of the sphere.

Plot2

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Example Question #32 : Geometric Measurement & Dimension

Find the volume of a sphere, where the radius is .

Possible Answers:

$V = 18432 \pi$

V = 18432

V = 13824

$V = 768 \pi$

$V = 13824 \pi$

Correct answer:

$V = 18432 \pi$

Explanation:

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

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

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

$V = 18432 \pi$

Thus the volume is, $18432 \pi$

Here is a picture representation of the sphere.

Plot6

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Example Question #406 : High School: Geometry

Find the volume of a sphere, where the radius is .

Possible Answers:

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

$V = 12167 \pi$

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

V = 12167

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

Correct answer:

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

Explanation:

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

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

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

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

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

Here is a picture representation of the sphere.

Plot12

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Example Question #41 : Geometric Measurement & Dimension

Find the radius of a sphere, where the volume is 1658 . Round your answer to digits.

Possible Answers:

r = 62.50

$r = \frac{2487 \pi}{2}$

$r = \frac{2487}{2}$

r = 15.75

r = 7.91

Correct answer:

r = 15.75

Explanation:

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

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

Since we are given the volume ( $\uptext{V}$ ), we can plug it into the equation.

$1658 = \frac{4 \pi}{3} r^{3}$

Now we can solve for $\uptext{r}$ .

Now we divide by $\frac{4 \pi}{3}$ on each side.

Now our equation is

$r^{3} = \frac{2487 \pi}{2}$

To solve for $\uptext{r}$ , we need to take the cube root on each side.

r = 15.75

Here is a picture representation of our sphere.

Plot3

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Example Question #42 : Geometric Measurement & Dimension

Find the radius of a hemisphere, where the volume is 2822 .
Round your answer to digits.

Possible Answers:

r = 4233

$r = \frac{4233}{\pi}$

r = 11.05

r = 115.32

r = 10.74

Correct answer:

r = 11.05

Explanation:

Before we find the radius of a hemisphere, we need to recall the equation.

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

Since we are given the volume ( $\uptext{V}$ ), we can plug it into the equation.

$2822 = \frac{2 \pi}{3} r^{3}$

Now we can solve for $\uptext{r}$ .

Now we divide by $\frac{2 \pi}{3}$ on each side.

Now our equation is

$r^{3} = \frac{4233}{\pi}$

To solve for $\uptext{r}$ , we need to take the cube root on each side.

r = 11.05

Here is a picture of the hemisphere.

Plot4

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Example Question #2 : Cylinders, Pyramids, Cones, And Spheres Volume Formulas: Ccss.Math.Content.Hsg Gmd.A.3

Find the radius of a hemisphere, where the volume is 1990.
Round your answer to digits.

Possible Answers:

r = 96.84

r = 9.83

$r = \frac{2985}{\pi}$

r = 9.84

r = 2985

Correct answer:

r = 9.83

Explanation:

Before we find the radius of a hemisphere, we need to recall the equation.

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

Since we are given the volume ( $\uptext{V}$ ), we can plug it into the equation.

$1990 = \frac{2 \pi}{3} r^{3}$

Now we can solve for $\uptext{r}$ .

Now we divide by $\frac{2 \pi}{3}$ on each side.

Now our equation is

$r^{3} = \frac{2985}{\pi}$

To solve for $\uptext{r}$ , we need to take the cube root on each side.

r = 9.83

Here is a picture representation of the hemisphere.

Plot5

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Example Question #41 : Geometric Measurement & Dimension

Find the radius of a hemisphere, where the volume is 1352 .
Round your answer to digits.

Possible Answers:

r = 79.82

$r = \frac{2028}{\pi}$

r = 8.64

r = 2028

r = 8.93

Correct answer:

r = 8.64

Explanation:

Before we find the radius of a hemisphere, we need to recall the equation.

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

Since we are given the volume ( $\uptext{V}$ ), we can plug it into the equation.

$1352 = \frac{2 \pi}{3} r^{3}$

Now we can solve for $\uptext{r}$ .

Now we divide by $\frac{2 \pi}{3}$ on each side.

Now our equation is

$r^{3} = \frac{2028}{\pi}$

To solve for $\uptext{r}$ , we need to take the cube root on each side.

r = 8.64

Here is a picture of what the hemisphere look like.

Plot7

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Example Question #41 : Geometric Measurement & Dimension

Find the radius of a hemisphere, where the volume is 1909 .
Round your answer to digits.

Possible Answers:

$r = \frac{5727}{2}$

$r = \frac{5727}{2 \pi}$

r = 94.85

r = 9.74

r = 9.70

Correct answer:

r = 9.70

Explanation:

Before we find the radius of a hemisphere, we need to recall the equation.

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

Since we are given the volume ( $\uptext{V}$ ), we can plug it into the equation.

$1909 = \frac{2 \pi}{3} r^{3}$

Now we can solve for $\uptext{r}$ .

Now we divide by $\frac{2 \pi}{3}$ on each side.

Now our equation is

$r^{3} = \frac{5727}{2 \pi}$

To solve for $\uptext{r}$ , we need to take the cube root on each side.

r = 9.70

Here is a picture of the hemisphere.

Plot8

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Example Question #41 : Geometric Measurement & Dimension

Find the radius of a sphere, where the volume is 1897 .
Round your answer to digits.

Possible Answers:

$r = \frac{5691}{4}$

$r = \frac{5691 \pi}{4}$

r = 66.85

r = 16.47

r = 8.18

Correct answer:

r = 16.47

Explanation:

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

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

Since we are given the volume ( $\uptext{V}$ ), we can plug it into the equation.

$1897 = \frac{4 \pi}{3} r^{3}$

Now we can solve for $\uptext{r}$ .

Now we divide by $\frac{4 \pi}{3}$ on each side.

Now our equation is

$r^{3} = \frac{5691 \pi}{4}$

To solve for $\uptext{r}$ , we need to take the cube root on each side.

r = 16.47

Here is a picture of the sphere.

Plot9

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Common Core: High School - Geometry : Cylinders, Pyramids, Cones, and Spheres Volume Formulas: CCSS.Math.Content.HSG-GMD.A.3

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

All Common Core: High School - Geometry Resources

Example Questions

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

Example Question #2 : Cylinders, Pyramids, Cones, And Spheres Volume Formulas: Ccss.Math.Content.Hsg Gmd.A.3

Example Question #32 : Geometric Measurement & Dimension

Example Question #406 : High School: Geometry

Example Question #41 : Geometric Measurement & Dimension

Example Question #42 : Geometric Measurement & Dimension

Example Question #2 : Cylinders, Pyramids, Cones, And Spheres Volume Formulas: Ccss.Math.Content.Hsg Gmd.A.3

Example Question #41 : Geometric Measurement & Dimension

Example Question #41 : Geometric Measurement & Dimension

Example Question #41 : Geometric Measurement & Dimension

All Common Core: High School - Geometry Resources

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