Question

The volume of a cone is 3x* cubic units and its height is x units.
Which expression represents the radius of the cone's base, in units?
O 3x
6x
370x2
O 90X2
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Answer 1

Answer:

The radius of a cone is $\dfrac{3}{\sqrt{\pi} }\ \text{units}$.

Step-by-step explanation:

The formula of the volume of a cone is given by :

$V=\dfrac{1}{3}\pi r^2 h$

r is radius of cone

h is height of cone

We have,

Volume of a cone is 3x cubic units and height is x units. Putting the values of volume and height such that,

$r=\sqrt{\dfrac{3V}{\pi h}}\\\\r=\sqrt{\dfrac{3\times 3x}{\pi x}} \\\\r=\sqrt{\dfrac{3\times 3}{\pi}}\\\\r=\sqrt{\dfrac{9}{\pi}}\\\\r=\dfrac{3}{\sqrt{\pi} }\ \text{units}$

So, the radius of a cone is $\dfrac{3}{\sqrt{\pi} }\ \text{units}$.