Write the formula for the volume of a sphere.

\(\displaystyle V = \frac{4}{3}\pi r^3\)

Substitute the radius into the equation.

\(\displaystyle V = \frac{4}{3}\pi (\frac{3}{4}\pi)^3= \frac{4}{3}\pi (\frac{3}{4}\pi)(\frac{3}{4}\pi)(\frac{3}{4}\pi)\)

The answer is:  \(\displaystyle \frac{9}{16} \pi ^4\)

Write the formula for the volume of a sphere.

\(\displaystyle V= \frac{4}{3}\pi r^3\)

Substitute the radius.

\(\displaystyle V= \frac{4}{3}\pi (6)^3 = \frac{4}{3}\pi (6) (6) (6) = 288\pi\)

The answer is:  \(\displaystyle 288\pi\)

To find the volume of a sphere, we will use the following formula:

\(\displaystyle V = \frac{4}{3}\pi r^3\)

where r is the radius of the sphere. 

Now, we know the radius of the sphere is 6cm. So, we can substitute. We get

\(\displaystyle V = \frac{4}{3} \cdot \pi \cdot (6\text{cm})^3\)

\(\displaystyle V = \frac{4}{3} \cdot \pi \cdot 216\text{cm}^3\)

Now, the 3 and the 216 can both be divided by 3. So, we get

\(\displaystyle V= \frac{4}{1} \cdot \pi \cdot 72\text{cm}^3\)

\(\displaystyle V= 4 \cdot \pi \cdot 72\text{cm}^3\)

\(\displaystyle V = 4 \cdot 72\text{cm}^3 \cdot \pi\)

\(\displaystyle V = 288\text{cm}^3 \cdot \pi\)

\(\displaystyle V = 288\pi \text{ cm}^3\)

Write the formulas for the surface area and volume of a sphere.

\(\displaystyle A = 4\pi r^2\)

\(\displaystyle V=\frac{4}{3} \pi r^3\)

Substitute the surface area into the first formula and solve for the radius.

\(\displaystyle 4\pi = 4\pi r^2\)

Divide by \(\displaystyle 4\pi\) on both sides.

\(\displaystyle \frac{4\pi }{4\pi}= \frac{4\pi r^2}{4\pi}\)

\(\displaystyle 1=r^2\)

Square root both sides.

\(\displaystyle r=1\)

Substitute the radius into the volume formula.

\(\displaystyle V=\frac{4}{3} \pi (1)^3 = \frac{4}{3} \pi\)

The answer is:  \(\displaystyle \frac{4}{3} \pi\)

Write the formula for the volume of a sphere.

\(\displaystyle V=\frac{4}{3}\pi r^3\)

Substitute the radius.

\(\displaystyle V=\frac{4}{3}\pi (\pi ^6)^3= \frac{4}{3}\pi (\pi ^6) (\pi ^6) (\pi ^6)\)

The answer is:  \(\displaystyle \frac{4}{3}\pi ^{19}\)

You are 3D printing a ball which will be an integral piece to the project you are creating. If you need the ball to have a radius of 12cm, what volume of material will be required?

We are asked to find the volume of a sphere, to do so, we should use the formula for volume of a sphere.

\(\displaystyle V_{sphere}=\frac{4}{3} \pi r^3\)

So, let's plug in our radius and solve:

\(\displaystyle V_{sphere}=\frac{4}{3} \pi (12cm)^3=\frac{4}{3} \pi 1728cm^3=7234.56 cm^3\)

So our answer is:

\(\displaystyle 7234.56 cm^3\)

You are given a spherical floating speaker for your birthday. If the speaker has a radius of 5 inches, what is its volume?

We need to find the volume of a sphere. To do so, we need the following formula:

\(\displaystyle V=\frac{4}{3}\pi r^3\)

We know r is 5, so just plug and simplify

\(\displaystyle V=\frac{4}{3}\pi (5in)^3\approx 523.56in^3\)

The formula for the surface area \(\displaystyle A\) of a sphere, given its radius \(\displaystyle r\), is

\(\displaystyle A= 4 \pi r^{2}\).

Set \(\displaystyle A = 20 \pi\) and solve for \(\displaystyle r\) to get the radius.

\(\displaystyle 4 \pi r^{2} = 20 \pi\)

Divide both sides by \(\displaystyle 4 \pi\):

\(\displaystyle \frac{4 \pi r^{2}}{4 \pi} = \frac{20 \pi}{4 \pi}\)

\(\displaystyle r^{2} = 5\)

Take the positive square root of both sides to obtain the radius:

\(\displaystyle r = \sqrt{5}\)

The formula for the volume \(\displaystyle V\) of a sphere, given its radius \(\displaystyle r\), is

\(\displaystyle V = \frac{4 \pi r^{3}}{3}\)

Substitute \(\displaystyle \sqrt{5}\) for \(\displaystyle r\) in this formula and evaluate the expression:

\(\displaystyle V = \frac{4 \pi (\sqrt{5})^{3}}{3}\)

\(\displaystyle = \frac{4 \pi \cdot \sqrt{5}\cdot \sqrt{5} \cdot \sqrt{5}}{3}\)

\(\displaystyle = \frac{4 \pi \cdot5 \cdot \sqrt{5}}{3}\)

\(\displaystyle = \frac{20 \pi \sqrt{5}}{3}\)

Recall how to find the volume of a sphere:

\(\displaystyle \text{Volume}=\frac{4}{3}\pi r^3\)

Plug in the given radius to solve for the volume.

\(\displaystyle \text{Volume}=\frac{4}{3}\pi (8^3)=\frac{2048\pi}{3}=2144.66\)

Make sure to round to two places after the decimal point.

The formula for the volume of a sphere is \(\displaystyle (4/3)\Pi r^3\), with \(\displaystyle r\) standing for radius. Since you know that the radius of the sphere is \(\displaystyle 3\), all you have to do is plug in \(\displaystyle 3\) for \(\displaystyle r\) and solve. Once you do that you learn that the volume is \(\displaystyle 36\Pi\).