Question

The height of a cone is twice the radius of its base. What expression represents the volume of the cone, in cubic units?

Answer 1

Answer:

Step-by-step explanation:

Radius  = r units

Height = 2r

Volume of cone = (1/3)πr²h

$=\frac{1}{3}*\pi*r^{2}*(2r)\\\\=\frac{2}{3}\pi r^{3}$

Answer 2

Answer:

A. $V = \frac{2}{3}\pi x^3$

Step-by-step explanation:

Formula for volume of a cone: $V = \frac{1}{3}\pi r^2h$, where we know r = x, and h = 2x.

We can substitute the variables in the formula to find the expression that represents the total volume of the cone.

$V = \frac{1}{3}\pi r^2h\\V = \frac{1}{3}\pi x^2*2x\\V = \frac{1}{3}\pi 2x^3$Which simplifies into:

A. $V = \frac{2}{3}\pi x^3$