Question

The volume of a cone having radius 2 cm and height 6 cm is _________$c{m^3}$
A. $14\pi $
B. $12\pi $
C. $8\pi $
D. $16\pi $

Answer 1

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.