Question

The volume of a cone is 3rx? cubic units and its height is x units. Which expression represents the radius of the cone's base, in units?
O 3πx
O 6πx
O 3πx2
O 9πx2​

Answer 1

Answer:

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

Volume of cone with radius 'r' and height 'h' = $\frac{1}{3}\pi r^2h$

Equating the given volumes, we get

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

$r^2h=3$ × $3x^3$

$r^2h=9 x^3$

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

Therefore, $r^2x=9x^3$

$r^2=9x^2$

Therefore, $r=3 x$

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