Question

The formula to find the volume of cone is:
A. $\dfrac{4}{3}\pi {{r}^{2}}h$
B. $\pi {{r}^{2}}h$
C. $\dfrac{1}{3}\pi {{r}^{2}}h$
D. $4\pi {{r}^{2}}h$

Answer 1

Hint: A cone is a three-dimensional figure with one circular base. A curved surface connects the base and the vertex. The volume of a 3-dimensional solid is the amount of space it occupies. Volume is measured in cubic units $\left( i{{n}^{3}},f{{t}^{3}},c{{m}^{3}},{{m}^{3}} \right)$ etc. Be sure that all the measurements are in the same unit before computing the volume.

Complete step by step answer:
In this question, we have been asked to find the formula for the volume of cones. So,we will start with the following figure of a cone.

The cone’s volume is exactly one third of the volume of a cylinder with the same base and height.

So, the formula for the volume of a cylinder is given as,
$V=B.h$
Where B is the base and h is the height of the cylinder. So, we know that the area of a circle or Base is $\pi {{r}^{2}}$. So, the formula for the base of the cylinder would be,
$V=\pi {{r}^{2}}h$
And the volume of the cone is $\dfrac{1}{3}$ of the volume of the cylinder. If the base and the height of cylinder and cone is same, then the volume of the cone would be,
$V=\dfrac{1}{3}\pi {{r}^{2}}h$
Here, r is the radius of the base and h is the height of the cone and cylinder.
Therefore, we find the formula for the volume of the cone to be $\dfrac{1}{3}\pi {{r}^{2}}h$.
So, the correct answer is “Option C”.

Note: The volume of the cylinder is $\pi {{r}^{2}}h$. We can think that the cone is a part of the cylinder. If we put the cone in the cylinder of same height and same base and if we compare the volume of both cone and cylinder, then we see that the volume of the cone is less than that of the cylinder. This is exactly one third of the cylinder’s original volume.