The diameter of a cone is equal to the height of the cone. The volume of the cone is 7.0685 cm³. Find the radius of the cone. (Consider 26.9 $\approx$ 27)

Let the diameter of the base of the cone be d cm.

So, the height of the cone = d cm

The radius of the base = $\frac{d}{2}$

The volume of the cone = $\frac{1}{3}\times \mathrm{\pi }\times {\left(\frac{\mathrm{d}}{2}\right)}^2\times \mathrm{d}$

$=\frac{d^3\times \mathrm{\pi }}{12}$

$$\begin{gathered} \Rightarrow \frac{d^3\times \mathrm{\pi }}{12}=7.0685 \\ \Rightarrow d^3\approx 27 \\ \Rightarrow d=3 \\ \Rightarrow \frac{d}{2}=r=1.5 cm \end{gathered}$$