Answer
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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.
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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