Question

The base diameter and the height of a cone are both equal to x units.



Which expression represents the volume of the cone, in cubic units?

πx2
2πx3
πx2
πx3

Answer 1

By definition, the volume of a cone is given by:

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

Where,

r: cone circular base radius

h: height of the cone

Substituting values we have:

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

Rewriting the equation we have:

$V = (\frac{1}{3}) * (\pi) * (\frac{x^2}{4}) * (x)$

$V = (\frac{1}{12}) * (\pi) * (x ^ 3)$

Answer:

An expression that represents the volume of the cone, in cubic units is:

$V = (\frac{1}{12}) * (\pi) * (x ^ 3)$

Note: rewrite the options again.

Answer 2

The volume of the cone is

$\dfrac{1}{3}\pi x^{3}$

Cone

A shape that has a round base and a point at the top.

Given

The height and base circle of the cone are the same that is x units.

h is the height of the cone and

r is the radius of the base circle of the cone.

h = r = x units

We need to find the volume of the cone which is given by

$\rm Volume\ of\ the\ cone\ = \frac{1}{3} *area\ of\ circle * height\ of\ the\ cone$

$Volume\ of\ the\ cone = \frac{1}{3} *\pi r^{2} h$

$Volume\ of\ the\ cone=\frac{1}{3} \pi x^{2} *x$

$Volume\ of\ the\ cone=\frac{1}{3} x^{3}$

Thus, the volume of a cone is

$\dfrac{1}{3} \pi x^{3}$

To more about the cone link is given below.

https://brainly.com/question/1315822