First, convert the dimensions to cubic centimeters by multiplying by \(\displaystyle 100\): the cone has height \(\displaystyle 300cm\), and its base has radius \(\displaystyle 200cm\).

\(\displaystyle 3m*\frac{100cm}{1m}=300cm\ \ \2m*\frac{100cm}{1m}=200cm\)

Its volume is found by using the formula and the converted height and radius.

\(\displaystyle V=\frac{1}{3} \pi r^{2}h\)

\(\displaystyle V=\frac{1}{3} \pi (200cm)^{2} ( 300cm )\approx 12,566,371 \; \textrm{cm}^{3}\)

Now multiply this by \(\displaystyle 0.45\frac{g}{cm^3}\) to get the mass.

\(\displaystyle m=V*\rho\)

\(\displaystyle 12,566,371cm^3*0.45\frac{g}{cm^3} \approx 5,654,867g\)

Finally, convert the answer to kilograms.

\(\displaystyle 5654867g *\frac{1kg}{1,000g} \approx 5,655kg\)

The volume of a cone is:

\(\displaystyle Volume=\frac{1}{3}\pi r^2h\)

where \(\displaystyle r\) is the radius of the circular base, and \(\displaystyle h\) is the height (the perpendicular distance from the base to the vertex).

As the circular base area is \(\displaystyle \pi r^2\), so we can rewrite the volume formula as follows:

\(\displaystyle Volume =\frac{A\times h}{3}\)

where \(\displaystyle A\) is the circular base area and known in this problem. So we can write:

\(\displaystyle Volume =\frac{A\times h}{3}=\frac{4\times 4}{3}=\frac{16}{3}\approx 5.333 m^3\)

We know that density is defined as mass per unit volume or:

\(\displaystyle \rho =\frac{m}{v}\)

Where \(\displaystyle \rho\) is the density; \(\displaystyle m\) is the mass and \(\displaystyle v\) is the volume. So we get:

\(\displaystyle m=\rho v=1000\times 5.333=5333 Kg\)

The volume of a cone is:

\(\displaystyle Volume=\frac{1}3{}\pi r^2h\)

where \(\displaystyle r\) is the radius of the circular base, and \(\displaystyle h\) is the height (the perpendicular distance from the base to the vertex).

\(\displaystyle Volume=\frac{1}3{}\pi r^2h =\frac{1}3{}\pi t^2\times 2t=\frac{2}{3}\pi t^3\)

The volume of a cone is given by:

\(\displaystyle Volume=\frac{1}{3}\pi r^2h\)

where \(\displaystyle r\)is the radius of the circular base, and \(\displaystyle h\) is the height; the perpendicular distance from the base to the vertex. Substitute the known values in the formula:

\(\displaystyle Volume=\frac{1}{3}\pi r^2h\Rightarrow 8\pi=\frac{1}{3}\pi\times (2t)^2\times 3t\)

\(\displaystyle \Rightarrow 8\pi=4\pi t^3\Rightarrow t^3=2\Rightarrow t=\sqrt[3]{2}\)

First, divide the diameter in half to find the radius.

\(\displaystyle \frac{d}{2}=r\)

\(\displaystyle \frac{12}{2}=6\:m\)

Now, use the formula to find the volume of the cone.

\(\displaystyle \text{Volume}=\frac{1}{3}\pi r^2 h\)

\(\displaystyle \text{Volume}=\frac{1}{3}\pi \times 6^2\times4=\frac{1}{3}\pi \times 36\times4=\frac{144}{3}\pi=48\pi\:m^3\)

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 volume of a cylinder is:

 \(\displaystyle Volume=\pi r^2h\)

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

Since \(\displaystyle h=2r\), we can substitute that into the volume formula. So we can write:

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

\(\displaystyle 16\pi=\pi r^2\cdot (2r)\)

\(\displaystyle 16\pi =2\pi r^{3}\)

\(\displaystyle 16=2r^{3}\)

\(\displaystyle 8=r^{3}\)

\(\displaystyle r=2\)

So we get:

\(\displaystyle h=2r=2\times 2=4\)

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:

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