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**Hint:**We are given a cone of radius 2 cm and height 6 cm and we know that the volume of the cone with radius r and height h is given by $Volume = \dfrac{1}{3}\pi {r^2}h{\text{ }}cu.units$ and using the given radius and height we get the required volume.

**Complete step by step solution:**

We are asked to find the volume of a cone

We are given that the radius of the cone is 2 cm

And the height of the cone is 6 cm

We know that the volume of the cone with radius r and height h is given by

$ \Rightarrow Volume = \dfrac{1}{3}\pi {r^2}h{\text{ }}cu.units$

Here

$

\Rightarrow r = 2cm \\

\Rightarrow h = 6cm \\

$

Using this in the formula we get

$

\Rightarrow Volume = \dfrac{1}{3}\pi \times 2\times 2\times 6 \\

\Rightarrow Volume = \pi \times 2\times 2\times 2 \\

\Rightarrow Volume = \pi \times 8 \\

\Rightarrow Volume = 8\pi c{m^3} \\

$

Hence the volume of the cone with radius 2 cm and height 6 cm is $8\pi c{m^3}$

**Therefore the correct answer is option C.**

**Note :**

1) Here we don’t substitute the value of $\pi $ as all the options given contain $\pi $.

2) The volume V of a cone with radius r is one-third the volume of the cylinder with the same base and height.

3) The formula for the volume of an oblique cone is the same as that of a right one.

4) The volumes of a cone and a cylinder are related in the same way as the volumes of a pyramid and a prism are related.

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