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:

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

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

Equating the given volumes, we get

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

$r^{2} h =3 \times 3 x^{3}$

$r^{2} h =9 x^{3}$

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.

Answer 2

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

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