Question

The volume of a cylinder is 180 cubed meters. What is the volume of a cone with the same radius and height as the cylinder?

Answer 1

60 cubic meters will be the volume of such cone.

Explanation:

Formula for volume of a cylinder:

`V = \pi r^(2) h ...... (1)`

Where
`r` is the radius of base of cylinder

and
`h` is the height of cylinder

V = 180 cubic meters

Formula for volume of a cone:

`V' = (1)/(3)\pi R^(2) H ...... (2)`

Where
`R` is the radius of base of cone

and
`H` is the height of cone

Now, it is given that height and radius of cone are equal.

`r = R\\h =H`

Putting the values in equation (2):

`V' = (1)/(3)\pi r^(2) h`

Using equation (1):

`V' = (1)/(3) * V`

Putting V = 180 cubic meters

`\Rightarrow V' = (1)/(3) * 180\\\Rightarrow V'=60 \text { cubic meters}`

Hence, 60 cubic meters will be the volume of such cone.