Question

given a soda can with a volume of 15 and a diameter of 2 what is the volume of a cone that fits perfectly inside the can

Answer 1

`5cm^(3)`

Explanation:

This problem bothers on the mensuration of solid shapes, cone an cylinder.

from the formula of cylinder and cone we can see that the volume of a cone is 3 times smaller than that of a cylinder

`volume=\pi r^(2) h`....................cylinder

`volume= (1)/(3) \pi r^(2)h`.................cone

assuming all units in (cm)

Given data.

Volume of cylinder =
`15cm^(3)`

Diameter d=
`2cm`

Radius r =
`(d)/(2)`
`= (2)/(2) = 1cm`

Height h= ??

we know that the expression for the volume of a cylinder is

`volume=\pi r^(2) h`

we can substitute our given data to find the height h

`15= 3.142*1^(2)*h\\15= 3.142h`

divide both side by 3.142 we have

`h= (15)/(3.142)\\ h= 4.77cm`

We can now use this height
`4.77cm` and radius
`1cm` to find the equivalent volume of a cone.

the expression for the volume of a cone is

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

substituting our data into the expression we have

`volume= (3.142*1^(2*) 4.77)/(3) \\volume= (15)/(3) \\voulume = 5cm^(3) \\`