Question

The base diameter and the height of a cone are both equal to

X units.
Which expression represents the volume of the cone, in
cubic units?
Piex2
2piex3
o 1/3piex?
o 1/12piex

Answer 1

For this case we know that the diameter and height of a cone are both equal. That means:

`h = D=x`

With
`D =2r` with r the radius. The volume of a cone is given by:

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

And for this case we know that h =x and
`x =2r` so then
`r= (x)/(2)`

And replacing we got:

`V= (1)/(3) ((x)/(2))^2 (x)= (1)/(12) x^3`

And the best option would be:

1/12pix^3

Explanation:

For this case we know that the diameter and height of a cone are both equal. That means:

`h = D=x`

With
`D =2r` with r the radius. The volume of a cone is given by:

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

And for this case we know that h =x and
`x =2r` so then
`r= (x)/(2)`

And replacing we got:

`V= (1)/(3) ((x)/(2))^2 (x)= (1)/(12) x^3`

And the best option would be:

1/12pix^3