Question

The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?

Answer 1

By definition, the volume of a cone is given by:
 $V = (1/3) * (\pi) * (r ^ 2) * (h)$
 Where,
 r: radius of the circular base
 h: height of the cone
 Let's define a variable:
 x: diameter of the base
 We have then that the radio is:
 $r = x / 2$
 The height is:
 $h = x$
 Substituting values:
 $V = (1/3) * (\pi) * ((x / 2) ^ 2) * (x)$
 Rewriting:
 $V = (1/3) * (\pi) * (x ^ 2/4) * (x) V = (1/12) * (\pi) * (x ^ 3)$
 Answer:
 An expression that represents the volume of the cone, in cubic units is:
 $V = (1/12) * (\pi) * (x ^ 3)$