The volume of a cylinder is the base multiplied by the height or length.  The base is the area of a circle, which is \(\displaystyle \pi r^{2}\).  Here, the radius is 2.  The diameter is 4. Three times the diameter is 12.  The height or length is 12. So, the answer is  \(\displaystyle 48\pi\).

The volume of a right cylinder with radius \(\displaystyle r=2\) and height \(\displaystyle h=6\) is:

 \(\displaystyle \pi r^2 h = \pi (2)^2 (6) = 24 \pi\)

Since the glass is only 75% full, only 75% of the interior volume of the glass is occupied by water. Therefore the volume of the water is:

\(\displaystyle 24 \pi \times ( 75 / 100 ) = 24 \pi (0.75) = 18 \pi\)

Using the circumference, we can find the radius of the circle. The equation for the circumference is \(\displaystyle 2\pi r\); therefore, the radius is 2.

Now we can find the area of the circle using \(\displaystyle \pi r^{2}\). The area is \(\displaystyle 4\pi\).

Finally, the surface area consists of the area of two circles and the area of the mid-section of the cylinder: \(\displaystyle 2\cdot 4\pi +4\pi h=16\pi\), where \(\displaystyle h\) is the height of the cylinder.

Thus, \(\displaystyle h=2\) and the volume of the cylinder is \(\displaystyle 4\pi h=4\pi \cdot 2=8\pi\).

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is \(\displaystyle Volume\:of\:cylinder= r^{2}*\pi*height\:of\:cylinder\)

In this example the height is 52 and the radius is 5 which we plug into our equation which will look like this \(\displaystyle Volume\:of\:cylinder= 5^{2}*\pi*52\)

We then square the 5 to get \(\displaystyle Volume=25*\pi*52\)

Then perform multiplication to get \(\displaystyle Volume=1300\pi\)

SA_cylinder = 2πrh + 2πr² = 2π(2)(10) + 2π(2)² = 40π + 8π = 48π cm²

In order to calculate the volume of a cylinder, we must utilize the formula \(\displaystyle V=\pi r^{2}h\). We were given the radius, \(\displaystyle \dpi{100} r=3cm\), and the height, \(\displaystyle \dpi{100} h=27cm\).

Insert the known variables into the formula and solve for volume \(\displaystyle \dpi{100} V\).

\(\displaystyle V=\pi *(3cm)^{2}*27cm\)

\(\displaystyle V=\pi*9cm^{2}*27cm\)

\(\displaystyle V=243\pi cm^{3}\)

In essence, we find the area of the cylinder's circular base, \(\displaystyle \dpi{100} A=\pi r^{2}\), and multiply it by the height.

In order to calculate the volume of a cylinder, we must utilize the formula \(\displaystyle V=\pi r^{2}h\). We were given the radius, \(\displaystyle \dpi{100} \dpi{100} r=\pi\), and the height, \(\displaystyle \dpi{100} \dpi{100} h=10\).

Insert the known variables into the formula and solve for volume \(\displaystyle \dpi{100} V\).

\(\displaystyle \dpi{100} V=\pi *(\pi)^{2}*10\)

\(\displaystyle \dpi{100} V=\pi*\pi^{2}*10\)

\(\displaystyle \dpi{100} V=10\pi^{3}\)

In essence, we find the area of the cylinder's circular base, \(\displaystyle \dpi{100} A=\pi r^{2}\), and multiply it by the height.

In order to solve this problem, one key fact needs to be understood.  A sphere will take up exactly \(\displaystyle \frac{2}{3}\) of the volume of a cylinder in which it is circumscribed. Therefore, if we find the volume of the sphere we can then solve for the volume of the cylinder.

First, we need to find the volume of the sphere.

\(\displaystyle \dpi{100} V=\frac{4}{3}\pi (2cm)^{3}\)

\(\displaystyle \dpi{100} \dpi{100} V_{sphere}=10\frac{2}{3}\pi cm^{3}\)

This equals \(\displaystyle \frac{2}{3}\) of the volume of the cylinder. Therefore,

\(\displaystyle \dpi{100} V_{cylinder}=\frac{3}{2}(10\frac{2}{3}\pi cm^{3})\)

\(\displaystyle \rightarrow 50.27cm^{3}\)

The volume of a cylinder is give by the equation \(\displaystyle \small V=\pi r^2h\).

In this example, \(\displaystyle \small h=6\) and \(\displaystyle \small r=3\).

\(\displaystyle V=\pi(3)^2(6)\)

\(\displaystyle V=\pi(9)(6)=54\pi\)

To find the volume of a cylinder we must know the equation for the volume of a cylinder which is

In this example the length is \(\displaystyle 12\) and the radius is \(\displaystyle 7\) so our equation will look like this \(\displaystyle V=(12)(\pi)(7^{2})\)

We then square the \(\displaystyle 7\) to get \(\displaystyle 7^{2}=49\)

Then perform multiplication to get \(\displaystyle (49)(12)(\pi)=588\pi\)

The answer is \(\displaystyle 588\pi\).