Define dimensions

Given the ratio $r: h = 3: 1$, let $r = 3x$ and $h = x$.

$r = 3x, h = x$

Solve for x

Substitute $r$ and $h$ into the volume formula $V = \pi r^2 h = 9702$. So, $\frac{22}{7} \times (3x)^2 \times x = 9702$. Thus, $\frac{22}{7} \times 9x^3 = 9702$. Solving for $x^3$: $x^3 = \frac{9702 \times 7}{22 \times 9} = 343$. So, $x = \sqrt[3]{343} = 7$.

$x = 7$

Calculate dimensions

Since $x = 7$, the radius $r = 3 \times 7 = 21$ cm and height $h = 7$ cm.

$r = 21, h = 7$

Calculate CSA

The curved surface area is $CSA = 2 \pi r h = 2 \times \frac{22}{7} \times 21 \times 7$.

$CSA = 2 \times 22 \times 3 \times 7 = 924$