Question

The volume of a cone is 3πx3 cubic units and its height is x units.

Which expression represents the radius of the cone’s base, in units?

Answer 1

Answer: The volume given is 3Pi(x^3) and the radius is x. The formula for the volume of a cone is V= [1/3]Pi(r^2)*height => [1/3]Pi (r^2) x = 3Pi(x^3) => (r^2)x = 3*3(x^3) => (r^2)x = 9(x^3) => (r^2) = 9x^2 => r = sqrt[9x^2] = 3x.

So THE CORRECT Answer is: A) r = 3x

Step-by-step explanation: I just paid for this answer

Answer 2

It is given that the volume of a cone =
`3 \pi x^(3)` cubic units

Volume of cone with radius 'r' and height 'h' =
`(1)/(3) \pi r^(2)h`

Equating the given volumes, we get

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

`r^(2) h =3 * 3 x^(3)`

`r^(2) h =9 x^(3)`

It is given that the height is 'x' units.

Therefore,
`r^(2) x =9 x^(3)`

`r^(2) =9 x^(2)`

Therefore, r = 3x

So, the expression '3x' represents the radius of the cone's base in units.