The volume of a right circular cone is 196$$\pi\ $$ $$cm^{3}$$. If the area of its base is 154 $$cm^{2}$$, what is the vertical height of the cone? (in cm) [Use $$\pi = \frac{22}{7}$$]

If the area of its base is 154 $$cm^{2}$$.

area of its base = $$\pi\ \times\left(radius\right)^2$$

$$154=\frac{22}{7}\times\left(radius\right)^2$$

$$7=\frac{1}{7}\times\left(radius\right)^2$$

$$7^2=\left(radius\right)^2$$

radius of cone = 7 cm

The volume of a right circular cone is 196$$\pi\ $$ $$cm^{3}$$.

volume of a right circular cone = $$\frac{1}{3}\times\ \pi\ \times\ \left(radius\right)^2\ \times\ height$$

$$196\pi = \frac{1}{3}\times\ \pi\ \times\ \left(7\right)^2\ \times\ height$$

$$196=\frac{1}{3}\times\ 49\ \times\ height$$
$$4=\frac{1}{3}\times\ height$$
vertical height of cone = 12 cm