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

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Question

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

Answer

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.

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Question

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

Answer

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.

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Question

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

Answer

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.

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Question

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

Answer

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.

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Question

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

Answer

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.

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Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

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Question

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

Answer

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.

Here is a picture of the hemisphere.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

$1507 = \frac{2 \pi}{3} r^{3}$

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

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

Now our equation is

$r^{3} = \frac{4521}{2 \pi}$

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

Here is a picture of the hemisphere.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

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