To find the volume of the cone, we first need to determine the radius of the sphere from its volume and then use that to calculate the volume of the cone.
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere. We know the volume \( V \) is 72 m³, so we can set up the equation:
\[ \frac{4}{3} \pi r^3 = 72 \]
To find \( r^3 \), we solve for \( r^3 \):
\[ r^3 = \frac{72 \times 3}{4\pi} = \frac{216}{4\pi} = \frac{54}{\pi} \]
Now, taking the cube root:
\[ r = \left(\frac{54}{\pi}\right)^{1/3} \]
Next, we calculate the diameter of the sphere:
\[ \text{Diameter} = 2r \]
Now, we know that the height \( h \) of the cone is equal to the diameter of the sphere:
\[ h = 2r \]
The volume \( V_c \) of a cone is given by the formula:
\[ V_c = \frac{1}{3} \pi r^2 h \]
Substituting \( h = 2r \):
\[ V_c = \frac{1}{3} \pi r^2 (2r) = \frac{2}{3} \pi r^3 \]
Now, we can substitute \( r^3 \) back in:
\[ V_c = \frac{2}{3} \pi \left(\frac{54}{\pi}\right) = \frac{2 \times 54}{3} = \frac{108}{3} = 36 \]
Thus, the volume of the cone is:
\[ \boxed{36} \text{ m}^3 \]