Since volume is length times width times height, and every side on a cube is equal, multiply

\(\displaystyle 9\cdot 9\cdot 9=729\)

The volume of this cube is \(\displaystyle 729\).

The volume of a cube is the cube of its sidelength, which is also the sidelength of each square face. This sidelength is the square root of the area 64:

\(\displaystyle \sqrt{64}=8\) inches.

Multiply this by 2.5 to get the sidelength in centimeters:

\(\displaystyle 8\) \(\displaystyle \times 2.5\) \(\displaystyle = 20\) centimeters.

The cube of this is 

\(\displaystyle 20^{3}\)  \(\displaystyle =8000\) cubic centimeters

A cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. As a formula:

\(\displaystyle Volume=s^3\) where \(\displaystyle s\) is the length of any edge of the cube.

The Surface Area of a cube can be calculated as \(\displaystyle 6s^2\).

So we get:

Volume \(\displaystyle =s^3=5^3=125 in^3\)

Surface area\(\displaystyle =6s^2=6\times 5^2=6\times 25=150 in^2\)

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height or:

 \(\displaystyle Volume=\pi r^2h\)

where \(\displaystyle r\) is the radius of the circular end of the cylinder and \(\displaystyle h\) is the height of the cylinder. So we can write:

\(\displaystyle Volume=\pi r^2h=\pi \times 3^2\times 3=84.82in^3\)

The surface area of the cylinder is given by:

\(\displaystyle A=2\pi r^2+2\pi rh\)

where \(\displaystyle A\) is the surface area of the cylinder, \(\displaystyle r\) is the radius of the cylinder and \(\displaystyle h\) is the height of the cylinder. So we can write:

\(\displaystyle A=2\pi r^2+2\pi rh\)

\(\displaystyle A=2\pi (3)^2+2\pi \times 3\times 3\)

\(\displaystyle A=18\pi+18\pi\)

\(\displaystyle A=36\pi\)

\(\displaystyle A=113.10\)

The area of the end (base) of a cylinder is \(\displaystyle \pi r^2\), so we can write:

\(\displaystyle \pi r^2=16\pi\Rightarrow r^2=16\Rightarrow r=4\ inches\)

The height of the cylinder is half of the radius of the base of the cylinder, that means:

\(\displaystyle h=\frac{r}{2}=\frac{4}{2}=2\ inches\)

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height:

\(\displaystyle Volume=Area\times h=16\pi\times 2=32\pi\)

or

\(\displaystyle Volume=\pi r^2h=\pi\times 4^2\times 2=32\pi\)

The volume of a cylinder is:

\(\displaystyle V=\pi r^2h\)

where \(\displaystyle V\) is the volume of the cylinder, \(\displaystyle r\)  is the radius of the circular end of the cylinder, and \(\displaystyle h\) is the height of the cylinder.

So we can write:

\(\displaystyle V_{1}=\pi (r_{1})^2h_{1}\)

and

\(\displaystyle V_{2}=\pi (r_{2})^2h_{2}\)

Now we can summarize the given information:

\(\displaystyle r_{1}=\sqrt{3}\cdot r_{2}\)

\(\displaystyle h_{2}=4\cdot h_{1}\Rightarrow h_{1}=\frac{h_{2}}{4}\)

Now substitute them in the \(\displaystyle V_{1}\) formula:

\(\displaystyle V_{1}=\pi (\sqrt{3}r_{2})^2\times \frac{h_{2}}{4}\Rightarrow V_{1}=\frac{3}{4}\pi (r_{2})^2\times h_{2}\Rightarrow V_{1}=\frac{3}{4}V_{2}\)

The volume of a cylinder is:

\(\displaystyle V=\pi r^2h\)

where \(\displaystyle r\) is the radius of the circular end of the cylinder and \(\displaystyle h\) is the height of the cylinder. So we can write:

\(\displaystyle V_{1}=\pi (r_{1})^2h_{1}\)

\(\displaystyle V_{2}=\pi (r_{2})^2h_{2}\)

We know that 

\(\displaystyle h_{1}=h_{2}\)

and 

\(\displaystyle r_{1}=2r_{2}\).

So we can write:

\(\displaystyle V_{1}=\pi (r_{1})^2h_{1}=\pi (2r_{2})^2\cdot h_{2}=4\pi (r_{2})^2h_{2}\Rightarrow V_{1}=4V_{2}\)

The volume of a sphere, given its radius, is 

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

Set \(\displaystyle V = 1,000\), solve for \(\displaystyle r\), and double that to get the diameter.

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

\(\displaystyle r^{3} = \frac{1,000 \cdot 3 }{4\pi} \approx 238.7\)

\(\displaystyle r \approx \sqrt[3]{238.7} \approx 6.2\)

The diameter is twice this, or 12.4 yards.

The diameter of a sphere is \(\displaystyle 6t\) so the radius of the sphere would be \(\displaystyle 6t\div 2=3t\)

The volume enclosed by a sphere is given by the formula:

\(\displaystyle Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times (3t)^3=\frac{4}{3}\pi\times 27t^3\Rightarrow Volume=36\pi t^3\)