Given the surface area, we can solve for the radius and then solve for the volume.

4πr² = 256π

4r² = 256

r² = 64

r = 8

Now solve the volume equation, substituting for r:

V = (4/3)π(8)³

V = (4/3)π*512

V = (2048/3)π

V = 683π

To find your answer, we would use the formula:  C=2πr. We are given that C = 29.5. Thus we can plug in to get  [29.5]=2πr and then multiply 2π to get 29.5=(6.28)r.  Lastly, we divide both sides by 6.28 to get 4.70=r. Then we would plug into the formula for volume V=(4π〖(4.7)〗³) / 3   (The information given of 22 ounces is useless) 

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

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

\(\displaystyle V=\frac{4}{3}\pi(216)\)

\(\displaystyle V=288\pi\)

\(\displaystyle V_{cube}=(\text{side})^3=(4)^3=64\)

\(\displaystyle V_{sphere}=\frac{4}{3}\pi r^3=\frac{4}{3}\pi(3^3)=\frac{4}{3}\pi(27)=36\pi\)

\(\displaystyle V_{total}=64+36\pi\)

The formula for the volume of a sphere is:

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

where \(\displaystyle r\) = radius.  The diameter is 6 in, so the radius will be 3 in. 

The volume of a sphere = \(\displaystyle \frac{4}{3}\pi r^{3}\)

Radius is \(\displaystyle \frac{1}{2}\) of the diameter so the radius = 5.

\(\displaystyle V=\frac{4}{3}\pi5^{3}\)

or \(\displaystyle V=\frac{500}{3\pi}\)

which is approximately \(\displaystyle 167\pi\)

To find the volume of a sphere we use the sphere volume formula:

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

First we need to find the radius of the sphere. A sphere has a radius of half the diameter. So we see that \(\displaystyle 12/2 =6=r\).

Next we plug 6 in for our radius and get
\(\displaystyle V = \frac{4}{3}\pi 6^3=288\pi in^3\) 

(don't forget your units).

The formula for the volume of a sphere is:
\(\displaystyle v = \frac{4}{3}\pi * r^3\), thus we need to just determine the radius and plug it into the equation. Remember that \(\displaystyle 2r = d\) and so 

\(\displaystyle 6 = 2r \newline 3 = r\)

And plugging in we get \(\displaystyle \frac{108}{3}\pi \textup{in}^3\)

First find the radius from the surface area set the given surface area equal to the surface area formula and solve for the radius.
\(\displaystyle 576\pi = 4\pi r^2\)

\(\displaystyle 144\pi = \pi r^2 \newline 144 = r^2 \newline 12 = r\)

Now plug the radius into the volume formula:
\(\displaystyle V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi 12^3 = 2304 \pi\textup{ ft}^3\)

Define the radius of Autumn’s orange as r. The volume of her orange is \(\displaystyle \pi r^3\). Ariana’s orange has twice the radius of Autumn’s, so the radius of her orange is \(\displaystyle 2r\), and the volume is \(\displaystyle \pi(2r)^3 = 8\pi r^3\), which is 8 times larger than Autumn’s orange.