Calculate the radius

Given the base area is 38.5 cm², we solve for the radius r using the formula for the area of a circle: $\pi r^2 = 38.5$. Substituting $\pi = 22/7$, we get $\frac{22}{7} r^2 = 38.5$, so $r^2 = \frac{38.5 \times 7}{22} = 12.25$. Thus, $r = \sqrt{12.25} = 3.5$ cm.

$r = 3.5 \text{ cm}$

Calculate the height

Given the curved surface area (CSA) is 616 cm², we use the formula $2\pi rh = 616$. Substituting the known values: $2 \times \frac{22}{7} \times 3.5 \times h = 616$. Simplifying: $2 \times 22 \times 0.5 \times h = 616$, which gives $22 \times h = 616$. Therefore, $h = \frac{616}{22} = 28$ cm.

$h = 28 \text{ cm}$

Calculate the volume

Finally, calculate the volume using the formula $V = \text{Base Area} \times h$. We have $V = 38.5 \times 28 = 1078$ cm³.

$V = 1078 \text{ cm}^3$