Cylinders, Pyramids, Cones, and Spheres Volume Formulas: CCSS.Math.Content.HSG-GMD.A.3

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Geometry › Cylinders, Pyramids, Cones, and Spheres Volume Formulas: CCSS.Math.Content.HSG-GMD.A.3

Questions 1 - 10

1

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

$V = 972 \pi$

$V = 729 \pi$

$V = 108 \pi$

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

2

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

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

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

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.

Here is a picture of the sphere.

Plot9

3

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

$r = \frac{7113 \pi}{4}$

$r = \frac{7113}{4}$

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.

$2371 = \frac{4 \pi}{3} r^{3}$

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

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

Now our equation is

$r^{3} = \frac{7113 \pi}{4}$

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

Here is a picture of the sphere.

Plot10

4

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

$V = 18432 \pi$

$V = 13824 \pi$

$V = 768 \pi$

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

5

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

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

$V = 12167 \pi$

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

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

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

6

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

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

$V = 512 \pi$

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

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

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

7

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

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

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.

Here is a picture representation of the hemisphere.

Plot5

8

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

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

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

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.

Here is a picture representation of our sphere.

Plot3

9

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

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

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.

Here is a picture of the hemisphere.

Plot4

10

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

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

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.

Here is a picture of what the hemisphere look like.

Plot7

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