Question

if the height and base diameter of a cylinder are respectively' 'hm' and 'rm' then the volume of largest cone thacane be extracted from the cylinder​

Answer 1

Given:

If the height and base diameter of a cylinder are respectively' 'hm' and 'rm'

To find:

The volume of the largest cone that can be extracted from the cylinder​

Solution:

The height of the cylinder = h meter

The base diameter of the cylinder = r meter

∴ The base radius of the cylinder = $\frac{Diameter}{2} = \frac{r}{2} \:meter$

To extract the largest cone from the cylinder, we have

Height of the cylinder = Height of the cone = h meter

Base radius of the cylinder = Base radius of the cone = $\frac{r}{2}\:meter$

We know the formula of the volume of the cone is,

$\boxed{\bold{Volume\:of\:a\:cone = \frac{1}{3}\pi r^2h }}$

Now, using the above formula and substituting the value of height and radius, we get

The volume of the largest cone is,

= $\frac{1}{3}\times\pi \times (\frac{r}{2} )^2\times h$

= $\frac{1}{3}\times\pi \times \frac{r^2}{4}\times h$

= $\frac{1}{12}\times\pi \times r^2\times h$

= [$\bold{\frac{1}{12}\pi r^2 h}$] m³

Thus, the volume of the largest cone that can be extracted from the cylinder​ is $[\underline{\frac{1}{12}\pi r^2 h}]\:m^3$.

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