Question

A cylinder and a cone are of the same radius and of same height. What is the ratio of volume of cylinder to that of cone?

Answer 1

Hint: We have a cylinder and a cone having same radius \[r\] and same height \[h\], Firstly we know that volume of a cylinder of radius r and having height h is given by \[{{V}_{cyclinder}}=\pi {{r}^{2}}h\] , Also we know that volume of a cone having base radius r and height h i.e. from base to tip is given by \[{{V}_{cone}}=\dfrac{1}{3}\pi {{r}^{2}}h\]. Now to find the ratio of volumes of cylinder and cone all we need to do is to divide these volumes i.e.
\[\dfrac{{{V}_{cyclinder}}}{{{V}_{cone}}}\].

Complete step-by-step answer:
First, we need to know:
- What is volume?
→ Volume of a body is the space occupied by it i.e. suppose there is a stone then the space it takes when you hold it in hand is its volume.

Now, we know that volume of a cylinder having radius of the base as \[r\] and having length \[h\] is given by
\[{{V}_{cyclinder}}=\pi {{r}^{2}}h\]
Here \[{{V}_{cyclinder}}\] refers to the space occupied by the cylinder.
Similarly, we can give the volume of a cone having radius \[r\] and height \[h\] as,
\[{{V}_{cone}}=\dfrac{1}{3}\pi {{r}^{2}}h\]
Here \[{{V}_{cone}}\] denotes volume of cone.
Now to find the ratio we divide \[{{V}_{cyclinder}}\] by \[{{V}_{cone}}\].
\[\dfrac{{{V}_{cyclinder}}}{{{V}_{cone}}}=\dfrac{\pi {{r}^{2}}h}{\dfrac{1}{3}\pi {{r}^{2}}h}\]
\[\dfrac{{{V}_{cyclinder}}}{{{V}_{cone}}}=\dfrac{1}{\dfrac{1}{3}}\]
\[\dfrac{{{V}_{cyclinder}}}{{{V}_{cone}}}=\dfrac{3}{1}\]

Note: The student must be aware of volume and its physical significance; also the student must know and memorize the formula for volume of cone and cylinder. If the student mistakes one formula for the other it will result in a wrong answer. Some common mistakes committed by students include interchanging the terms of ratio, inability to understand length is height in case of cylinder.