The surface area of a sphere is found by the formula $\displaystyle SA=4\pi r^{2}$. We need to first convert the given diameter of $\displaystyle D=\pi$ to the sphere's radius.

$\displaystyle D=2r$

$\displaystyle \pi =2r$

$\displaystyle r=\pi/2$

Now, we can solve for surface area.

$\displaystyle \dpi{100} \dpi{100} SA=4\pi \left ( \frac{\pi }{2}\right)^{2}$

$\displaystyle =4\pi \cdot \frac{\pi^{2} }{4}$

$\displaystyle \dpi{100} \rightarrow \pi^{3}$

The volume of a sphere in terms of its radius $\displaystyle r$ is 

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

Substitute $\displaystyle V = 1,000$ and solve for $\displaystyle r$:

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

$\displaystyle \frac{4\pi r^3}{3} = 1,000$

$\displaystyle \frac{4\pi r^3}{3}\cdot \frac{3}{4\pi }= 1,000\cdot \frac{3}{4\pi }$

$\displaystyle r^3= \frac{3,000}{4\pi }$

$\displaystyle r=\sqrt[3]{ \frac{3,000}{4\pi }} \approx 6.20 \textrm{ cm }$

Substitute for $\displaystyle r$ in the formula for the surface area of a sphere:

$\displaystyle A = 4\pi r^2 \approx 4 \cdot \pi \cdot 6.20 ^2 \approx 483.6 \textrm{ cm}^{2}$

The standard equation to find the area of a sphere is $\displaystyle 4\Pi r^2$.

Substitute the given radius into the standard equation to get the answer:

$\displaystyle 4\Pi (4)^2=4\Pi (16)=64\Pi$

The standard equation to find the area of a sphere is 

$\displaystyle SA=4\pi r^2$

where $\displaystyle r$ denotes the radius. Plug in the given radius to find the surface area. 

$\displaystyle SA=4\pi (3)^2=4\cdot 9\cdot \pi =36\pi$

The formula for the surface area of a sphere is:

$\displaystyle SA = 4 \pi r^2$

where $\displaystyle r$ is the radius of the sphere.

Plugging in our values, we get:

$\displaystyle SA = 4 \pi (6m)^2$

$\displaystyle SA = 4 \pi (36m) = 144 \pi m^2$

The formula for the surface area of a sphere is:

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

Where $\displaystyle r$ is the radius of the sphere

Plugging in our values, we get:

$\displaystyle SA = 4 \pi (9m)^2$

$\displaystyle SA = 324 \pi m^2$

Calculate the slant height height of the cone using the Pythagorean Theorem. The height will be the height of the cone, the base will be the radius, and the hypotenuse will be the slant height.

$\displaystyle s^2=r^2+h^2$

$\displaystyle s^2=(5)^2+(12)^2=25+144=169$

$\displaystyle s=\sqrt{169}=13$

The surface area of the cone (excluding the base) is given by the formula $\displaystyle A=\pi rs$. Plug in our values to solve.

$\displaystyle A_{cone}=\pi(5)(13)=65\pi\ cm^2$

The surface area of a sphere is given by $\displaystyle A=4\pi r^2$ but we only need half of the sphere, so the area of a hemisphere is $\displaystyle A=2\pi r^2$.

$\displaystyle A_{hemisphere}=2\pi(5)^2=50\pi\ cm^2$

So the total surface area of the composite figure is $\displaystyle 65\pi\ cm^2+50\pi\ cm^2=115\pi\ cm^2$.

A hemisphere is half of a sphere.  The surface area is broken into two parts:  the spherical part and the circular base. 

The surface area of a sphere is given by $\displaystyle SA = 4\pi r^{2}$.

So the surface area of the spherical part of a hemisphere is $\displaystyle SA = 2\pi r^{2}$. 

The area of the circular base is given by $\displaystyle A = \pi r^{2}$.  The radius to use is half the diameter, or 2 cm.

To solve for the surface area of a sphere you must remember the formula:

First, plug the radius into the equation for $\displaystyle r$:

$\displaystyle SA=(4)(12^{2})(\pi)$

Since $\displaystyle (12^{2})=144$, the surface area is $\displaystyle (4)(144)(\pi)=576\pi$.

The answer is therefore $\displaystyle 576\pi$.

To find the diameter of a sphere we must use the equation for the volume of a sphere to find the radius which is half of the diameter.

The equation is

First we enter the volume into the equation yielding $\displaystyle 36\pi=(\frac{4}{3})(\pi)(r^{3})$

We then divide each side by  to get $\displaystyle 36=(\frac{4}{3})(r^{3})$

We then multiply each side by  to get $\displaystyle 27=r^{3}$

We then take the cubic root of each side to solve for the radius $\displaystyle \sqrt[3]{27}=\sqrt[3]{r^{3}}$

The radius is $\displaystyle r=3$

We then multiply the radius by 2 to find the diameter $\displaystyle 3*2=6$

The answer for the diameter is $\displaystyle 6$.